| Séminaire
Mathjeunes |
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Retour |
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| Archives (2008-2012) |
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| 2012- |
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2011-2012 |
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ZHONG Changlong(University of Ottawa) |
11h05 30/06/2012 |
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Annihilators of torsion of Chow groups of
homogeneous varieties |
1 de 1 |
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I will introduce some combinatorial constructions
based on root system, and use it to provide an
annihilator of torsion of gamma filtration of
homogeneous varieties. Then I will mention a main
application, which provides an annihilator of
torsion part of the Chow group of a twist form. This
is joint work with S. Baek and K. Zainoulline. |
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SM-081 |
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ZHONG Changlong(University of Ottawa) |
10h00 30/06/2012 |
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Comparison of Dualizing Complexes |
1 de 1 |
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In this talk I will introduce the dualizing
complexes constructed by Moser, Spiess, Sato and
Bloch (duality by Geisser), and talk about the
comparison of these complexes. |
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SM-080 |
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GAO Ziyang(Paris 11) |
10h00 23/06/2012 |
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On the André-Oort conjecture for the product of
modular curves |
1 de 1 |
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We give an unconditional proof of the André-Oort
conjecture for arbitrary products of modular curves.
Our approach uses the theory of o-minimal
structures, a part of Model Theory. The strategy is
proposed by J. Pila. |
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SM-079 |
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MA Li(Paris 6) |
10h00 16/06/2012 |
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p-adic Gross-Zagier formula |
1 de 1 |
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I will talk about Perrin-Riou's work on p-adic
Gross-Zagier formula. The formula relates the p-adic
height of a Heegner point on an elliptic curve with
the first derivative of a p-adic L function
associated to the curve. |
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SM-078 |
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JIANG Zhi(Pairs 11) |
10h00 26/05/2012 |
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An introduction to M-regular sheaves and GV-objects
on abelian varieties |
1 de 1 |
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SM-077 |
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XIE Junyi(Ecole Polytechniques) |
10h00 19/05/2012 |
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Periodic points of birational maps of projective
smooth surfaces |
1 de 1 |
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We introduce some basics on dynamics of surface
birational maps. And we prove that if the first
dynamical degree of a surface birational map is
greater than one, then the periodic points are
Zariski dense. |
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SM-076 |
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LU Huajun(CAS) |
10h30 31/03/2012 |
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Infinitesimal fiber of minimal regular models of
elliptic curves |
1 de 1 |
Let K be a discrete valuation field with ring of
integers O_{K}. Let \pi be a uniformizing element of
O_{K}. Let E be an elliptic curve over K. Let X be
the minimal regular model of E over O_{K}. For any
natural integer n, let X_{n}=X x Spec
O_{K}/(\pi^{n+1}). I will present the following two
topics:
1. The isomorphism class of X_{0} as a curve over
the residue field k=O_{K}/(\pi). (finer than
Kodiara-Neron classification)
2. The relation between X_{n} and X'_{n+m} where
m>0 and X' is the minimal regular model of E over
the ring O_{L} of integers of a finite galois
extension L/K. |
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SM-075 |
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FU Lie(ENS) |
10h00 24/03/2012 |
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Autour des cycles algébriques |
1 de 1 |
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J'introduirai les conjectures concernant les cycles
algébriques, notamment, la conjecture de
Bloch-Beilinson, la conjecture de Murre, la
conjecture de Hodge (usuelle ou généralisée ), les
conjecture standards, la conjecture de Bloch
(généralisée), la conjecture de nilpotence etc.
J'expliquerai des résultats connus, et les relations
entre ses conjectures. Si le temps permis, je vais
expliquer en plus de détails sur les résultats de
Kimura sur la conjecture de dimension finie de
Kimura-O'Sullivan et ses applications. |
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SM-074 |
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TIAN Ye(CAS) |
10h00 03/03/2012 |
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Relative trace formula proof of Gross-Zagier theorem |
1 de 1 |
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Jacquet gave a relative trace formula proof of
Waldspurger's formula. Based on his approach, we
gave a relative trace formula proof of
Gross-Zagier's theorem. This is joint work with
Xinyi Yuan and Wei Zhang. |
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SM-073 |
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HU Yong(Paris 11) |
10h00 25/02/2012 |
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Serre's Conjecture II for classical groups |
1 de 1 |
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Let k be a perfect field of cohomological dimension
2. Serre's Conjecture II on Galois cohomology
predicts that H^1(k, G)=1 for any semisimple simply
connected algebraic group G over k. The goal of this
talk is to introduce the machinery and sketch
Bayer-Fluckiger and Parimala's proof of this
conjecture for classical groups. |
| E.
Bayer-Fluckiger and R. Parimala, Galois cohomology
of the classical groups over fields of cohomological
dimension <= 2, Invent. math. 122, 195-229 (1995) |
SM-072 |
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LIANG Yongqi(Paris 11) |
10h00 11/02/2012 |
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Principe local-global pour les zéro-cycles: une
synthèse |
1 de 1 |
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Je vous raconterai l'histoire de la conjecture de
Colliot-Thélène et al. sur le principe local-global
pour les zéro-cycles sur les variétés algébriques
définies sur un corps de nombres. |
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SM-071 |
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SHEN Shu(Paris 11) |
10h00 03/12/2011 |
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Super connection, impaire classe de Chern et
C^\infty RRG |
1 de 1 |
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Je vais présenter une analogue du theoreme de
Riemann Roch Grothendieck pour l'image directe d'un
fibre plat par une submersion. |
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http://math.berkeley.edu/~lott/jams.pdf |
SM-070 |
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Jyoti Prakash SAHA(Paris 11) |
10h00 12/11/2011 |
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Control theorem for algebraic p-adic L-functions |
1 de 1 |
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Hida constructed a two-dimensional big Galois
representation $T$ with coefficients in a certain
Hecke algebra. This algebra has some special type of
primes, called arithmetic primes which correspond to
cusp forms. The representation $T$ when specialized
at an arithmetic prime $P$ gives the usual
two-dimensional representation $T(f_P)$ for the cusp
form $f_P$ corresponding to $P$. We will prove a
control theorem for the Selmer complex
$R\Gamma_f(T)$ for $T$ at arithmetic primes, in the
sense that, $R\Gamma_f(T) mod P = R\Gamma_f(T(f_P)$. |
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SM-069 |
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LEE Ting-Yu(Paris 6) |
10h30 05/11/2011 |
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Introduction to the arithmetic of classical groups |
1 de 1 |
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We focus on some basic facts about classical groups,
and the relative classification about central simple
algebra with involutions. Maybe not so arithmetic
flavored. |
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SM-068 |
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JIANG Xun(Paris 11) |
10h00 22/10/2011 |
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Géométrie algébrique et géométrie analytique |
1 de 1 |
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Sur le douzième exposé de SGA 1 (le mémoire de M2
dirigé par M.Raynaud). |
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GAGA |
SM-067 |
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| 2010-2011 |
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SHEN Shu(Paris 11) |
10h00 25/06/2011 |
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Autour du théorème de l'indice d'Atiyah-Singer II |
1 de 1 |
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C'est la deuxième partie de mon exposé sur le
théorème de l'indice d'Atiyah-Singer. Il se consacre
à montrer le théorème de Riemanne-Roch-Hirzebruch
par la méthode du noyau de la chaleur. Cette partie
est indépendante à la première partie de mon exposé. |
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SM-066 |
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SUN Zhe(Paris 11) |
10h00 18/06/2011 |
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Moduli spaces of convex projective structures on
surfaces and Higher Teichmüller Spaces |
1 de 1 |
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arxiv1004.2894 arXiv:math/0405348
arXiv:math/0311149 |
SM-065 |
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CHEN Miaofen(Paris 11) |
14h15 13/06/2011 |
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The determinant morphism for moduli spaces of
p-disivible groups in the GL_n case.(suite) |
2 de 2 |
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SM-064 |
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CHEN Miaofen(Paris 11) |
10h00 13/06/2011 |
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The determinant morphism for moduli spaces of
p-disivible groups in the GL_n case. |
1 de 2 |
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The moduli space of p-divisible groups is introduced
by Rapoport and Zink and can be considered as local
analogue of Shimura varieties. These spaces are
representable by formal schemes. The objective of
this talk is to study the geometrically connected
components of the generic fiber of such
Rapoport-Zink spaces with level structures. I will
begin with the fundamental definitions and try to
make this talk accessible to most of you. |
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SM-063 |
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David GRIMM(Universitaet Konstanz) |
10h30 12/06/2011 |
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Sums of squares in algebraic function fields |
1 of 1 |
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Not much is known about the relation of sums of
squares in a function field and its field of
constants. Suppose, for example, every sum of
squares in the latter can be written as a sum of $n$
squares for some natural number $n$, is the same
then true (with possibly a different $n$) for the
entire function field? We address related questions
in particular cases. |
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SM-062 |
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SUN Shenghao(Polytechnique) |
14h15 04/06/2011 |
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Hodge theory and intersection cohomology |
2 of 2 |
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SM-061 |
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SUN Shenghao(Polytechnique) |
10h00 04/06/2011 |
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Hodge theory and intersection cohomology |
1 of 2 |
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We start by reviewing the classical theory of Hodge
and Lefschetz on the singular cohomology of complex
algebraic manifolds. Then we present two approaches
to generalize the theory to arbitrary algebraic
varieties: Deligne's mixed Hodge structures and
Goresky-MacPherson's intersection cohomology. In
particular, we present the celebrated decomposition
theorem of BBDG, and give many examples. |
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SM-060 |
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SHEN Shu(Paris 11) |
10h00 07/05/2011 |
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Autour du théorème de l'indice d'Atiyah–Singer I |
1 de 1 |
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C'est une série des exposes comme une introduction
pour le théorème de l'indice d'Atiyah–Singer. En
gros, le théorème dit que pour un opérateur
elliptique, l'indice topologique égale l'indice
analytique. Dans un premier temps, on commence par
établir la théorie de Fredholm. Comme une
application la périodicité de Bott sera montre. |
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SM-059 |
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Arno KRET(Paris 11) |
10h00 30/04/2011 |
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Lambda-adic representations associated to some
simple Shimura varieties |
1 of 1 |
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We follow Kottwitz' construction of Galois
representations associated to the automorphic
representations which occur in the cohomology of
certain compact Shimura varieties in cases where no
endoscopy occurs. This is basically the content of
Kottwitz paper in Inventiones with the same title as
this talk. To prove that the construction is
"correct" we will use another result of Kottwitz
concerning the number of points of the Shimura
varieties over finite fields. This number of points
is expressed in a non-stable sum of orbital
integrals of rational conjugacy classes in the
reductive group. The proof of this formula and its
stabilization could be subject of a future talk or
talks. |
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SM-058 |
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SUN Shenghao(Polytechnique) |
10h00 05/03/11 |
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Sato-Tate for function fields |
1 of 1 |
We explain Deligne's setting for the
equidistributionproblem, and sketch the proof that
"(1) implies (2)", namely the meromorphic
continuation implies the non-vanishing. We then
discuss the Sato-Tate conjecture for function
fields, focusing on the case of elliptic curves.
Again I will try to make the talk accessible to a
general audience. |
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SM-057 |
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SUN Shenghao(Polytechnique) |
14h30 15/01/11 |
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L-function method and equidistribution problem
(Sato-Tate type of conjectures) |
2 of 2 |
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SM-056 |
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SUN Shenghao(Polytechnique) |
10h00 15/01/11 |
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L-function method and equidistribution problem
(Sato-Tate type of conjectures) |
1 of 2 |
abstract: The talk has two parts. In the first part,
we explain in a general setting how to deduce the
equidistribution of a sequence of conjugacy classes
in a particular type of locally compact groups from
the analytic properties of the L-functions attached
to representations of these groups. In the second
part, we will apply this general story to the
special cases in which arithmetic geometers are
interested, (hopefully) including both the number
field case and the function
field case. The approach we follow is due to Serre
and Deligne. |
| Analysts
are welcome too. |
SM-055 |
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WU Han(École polytechnique fédérale de Lausanne) |
10h00 12/12/2010 |
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傅立叶分析与表示论(Fourier analysis and representation
theory) |
1 of 2 |
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Abstract |
|
horaire exceptionnel :
dimanche SM en
partenariat avec un séminaire
secret d'analyse .... |
SM-054 |
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Javier FRESAN(Paris 13) |
14h30 04/12/2010 |
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Autour de la conjecture de Gross-Deligne |
2 de 2 |
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SM-053 |
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Javier FRESAN(Paris 13) |
10h00 04/12/2010 |
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Autour de la conjecture de Gross-Deligne |
1 de 2 |
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Cette série de deux exposés se donne pour but de
présenter le travail de V. Maillot et D. Roessler
autour de la conjecture de Gross-Deligne. Dans la
première séance on énoncera cette conjecture reliant
les périodes des variétés algébriques définies sur
les corps de nombres algébriques aux valeurs
spéciales de la fonction gamma. Ensuite, on montrera
comment des outils profonds de la géométrie
d'Arakelov, notamment le théorème de Riemann-Roch
arithmétique équivariant, permettent de démontrer
une version faible de la conjecture dans certains
cas. |
| B.
H. Gross, On the Periods of Abelian Integrals and a
Formula of Chowla and Selberg, Invent. Math. 45
(1978),
193-211.
V. Maillot, D. Roessler, On the periods of motives
with complex multiplication and a conjecture of
Gross-Deligne, Ann. of Math. 160 (2004),
727-754.
C. Soulé, Genres de Todd et valeurs aux entiers des
dérivées de fonctions L, Séminaire Bourbaki
2005/2006, Exp. 955, Astérisque 311 (2007), 75-98. |
SM-052 |
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SUN Shenghao(Polytechnique) |
10h00 13/11/2010 |
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On stacks |
1 de ? |
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SM-051 |
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LU Chengyuan(Paris
13)
Sauf si grève |
10h00 06/11/2010 |
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An introduction to a resolution to the modules of
lie algebra |
1 of 1 |
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We will introduce some elementary theories of
cohomology of Lie algebras and something around it. |
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SM-050 |
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LU Chengyuan(Paris 13) |
14h30 30/10/2010 |
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An introduction to a resolution to the modules of
lie algebra |
1 of 1 |
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We will introduce some elementary theories of
cohomology of Lie algebras and something around it. |
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annulé |
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Ariyan JAVANPEYKAR(Paris 11-Leiden) |
10h00 30/10/2010 |
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The Grothendieck-Riemann-Roch theorem and heights
for covers of surfaces with fixed branch locus |
2 of 2 |
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cf. 1 of 2 |
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notes |
SM-049 |
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Ariyan JAVANPEYKAR(Paris 11-Leiden) |
10h00 23/10/2010 |
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The Grothendieck-Riemann-Roch theorem and heights
for covers of surfaces with fixed branch locus |
1 of 2 |
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The first part of this talk will consist of
explaining the notions that go into the
statement of the Grothendieck-Riemann-Roch theorem:
Grothendieck's K_0-theory, intersection theory
and characteristic classes. Some basic examples will
be given. In my thesis I also give several
applications. The main application being to the
proof of a function field analogue of a conjecture
by Edixhoven-de Jong-Schepers, the second part of
this talk will consist mainly of discussing the
latter. |
|
notes |
SM-048 |
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| 2009-2010 |
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Zhi JIANG(ENS) |
10h10 17/04/2010 |
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Pluricanonical systems on certain projective
varieties |
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Pluricanonical systems are the central objects in
birational geometry. They are well understood on
surfaces since Bomberi's work in 70's. But
only recently, breakthrough in higher dimensions is
achieved by Hacon-McKernan, Takayama, Siu... I will
report some recent progress. |
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SM-047 |
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| Ting
Yu LEE(Paris-6) |
14h30 10/04/2010 |
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Groupe de Travail sur Groupes
Algébriques |
1 of 2 |
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GdT-GA04 |
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Cheng Yuan LU(Paris 13) |
14h00 27/03/2010 |
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An introduction to Moduli space of abelian varieties |
1 of 1 |
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We will understand the moduli space of abelian
varieties with certain level sturcture by using the
language of stacks. The course will contain an naive
introduction of stacks. |
| |
annulé |
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Wen Wei LI(Paris 7) |
10h10 27/03/2010 |
| Introduction
à la théorie de Bruhat-Tits II |
2 de 2 |
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SM-046 |
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Wen Wei LI(Paris 7) |
14h30 20/03/2010 |
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Introduction à la théorie de Bruhat-Tits |
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| L'immeuble
de Bruhat-Tits est un certain complexe simplicial
sur lequel un groupe réductif p-adique opère. Cette
structure combinatoire encode des informations fines
du groupe en question. On en esquissera
laconstruction et des propriétés importantes ainsi
que quelques applications, pour les groupes
réductifs en général si possible. Les canons sont
[BT1, BT2], tandis que [T] est souvent conseillé
comme le meilleur guide; je suivrai parfois [L] dans
l'exposé. |
[BT1]
F. Bruhat et J. Tits, Groupes réductifs sur un corps
local I, Publ. Math. IHES, 41 (1972).
[BT2] F. Bruhat et J. Tits, Groupes réductifs sur un
corps local II, Publ. Math. IHES, 60 (1984).
[T] J. Tits, Reductive Groups over Local Fields, in
Proc. Symp. Pure Math. vol. 33 part 1 ("Corvallis"
1977).
[L] E. Landvogt, A Compactification of the
Bruhat-Tits Building, Lecture Notes in Mathematics
1619, Springer-Verlag, 1996. |
SM-045 |
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Arno KRET(Paris 11) |
10h10 20/03/2010 |
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A
Lefschetz trace formula for the cohomology of
certain compact Shimura varieties |
1 of 1 |
Let (G,X) be a PEL-type Shimura datum, and \rho a
complex algebraic representation of G. To \rho is a
complex vector bundle L on the (analytical)
Shimura tower. Let f be a function of the Hecke
algebra of G(Q-hat) which is an elementary tensor of
the form f = tensor_v f_v such that there exists a
prime number v_0 such that f_v_0 is supported on the
regular elements of G(Q_v_0). Then we have an
"explicit" formula for the trace of f acting on the
alternating sum cohomology of L.
The talk will consist of 3 parts, first we will
introduce all the necessary notions in the above,
then we give the trace, and in the last part we will
give a detailed proof of this formula. The above
theorem is a result of Fargues, proved in his
thesis, Asterisque 291, chapter 6. Although we
intend to define the things we are talking about,
this talk will be somewhat technical and some
background on Shimura varieties and cohomology is
required. |
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SM-044 |
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Hao Ran WANG(Paris 6) |
10h10 06/03/2010 |
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$p$-adic unit ball and $p$-adic upper half plane |
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Abstract: This talk is about elementary
$p$-adic geometry. Two basic objects are
concerned: unit balls and upper half plane. I will
recall the basic notions in rigid analytic
geometry. I will give an explanation of the upper
half plane in this setting. You can think of these
objects as examples of some definitions in my
memoire.
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SM-043 |
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Xu SHEN(Paris-11) |
10h10 06/02/2010 |
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On the Geometry and Cohomology of Some PEL-type
Shimura Varieties-Talk 3. The cohomology of proper
Shimura varieties |
3 of 3 |
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3)- interlude about deformation of finite flat group
schemes (d'après Grothendieck-Illusie), formally
lifting the above constructions to characteristic
zero, Drinfeld level structures, interlude about
formal vanishing cycles (d'après Berkovich), the
isomorphism between pullbacks of vanishing cycles on
Shimura varieties and on Rapoport-Zink spaces, the
cohomology of Rapoport-Zink spaces, the cohomology
of proper Shimura varieties. |
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SM-042 |
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Xu SHEN(Paris-11) |
10h10 30/01/2010 |
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On the Geometry and Cohomology of Some PEL-type
Shimura Varieties-Talk 2. The geometry and
cohomology of Newton polygon stratas |
2 of 3 |
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2)- solpe filtration of p-divisible groups,
some distinguished central leaves, Igusa varities,
a system of covering of the Newton stratas by
Igusa varieties and truncated Rapoport-Zink
spaces, the finiteness of the morphisms,
application to cohomology.
|
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SM-041 |
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Xu SHEN(Paris-11) |
10h10 23/01/2010 |
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On the Geometry and Cohomology of Some PEL-type
Shimura Varieties-Talk 1. Basics about
PEL-type Shimura varieties (unramified) |
1 of 3 |
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This series of talks will be
mainly based on my M2 memoire of the
works of Elena Mantovan, which generalizes Oort's
almost product structure about the Newton polygon
stratas of Siegel modular varieties, and
Harris-Taylor's notion of Igusa varieties and
their first basic identity for some special simple
unitary Shimura varieties, to the PEL setting. It
can also be viewed as a supplement and improvement
of Rapoport-Zink's uniformization of PEL-type
Shimura varieties.
There are some relevant and interesting
topics, such as Chai's theory of canonical
coordinates and p-adic monodromy of the central
leaves, the work of Fargues on the cohomology of
Rapoport-Zink spaces, the technique of counting
points and stable trace formula method for Igusa
varieties (initiated from Kottwitz, Langlands,
etc, adapted to Igusa varieties by
Harris-Taylor, and further developed by Shin).
However, due to the time limitation, we will not
touch these subjects.
1)- PEL-type Shimura varieties, basic examples,
representability (via geometric invariant theory
& Artin' criterion by local moduli
respectively), complex period morphism and complex
uniformization, local systems, Newton polygon
stratification, Rapoport-Zink spaces, p-adic period
morphism and p-adic uniformization. |
|
le mémoire- demandez-le à
l'auteur |
SM-040 |
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Cheng Yuan LU(Paris-13) |
14h30 16/01/2010 |
|
A Narrative of Serrre
Conjecture |
1 of 1 |
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J.-P. Serre, Sur les représentations
modulaires de degré 2 de
Gal(\bar{Q}/Q) |
SM-039 |
|
| Arno
KRET(Paris-11) |
10h30 16/01/2010 |
|
Le groupe fondamental des variétés
abéliennes |
1 de 1 |
|
On
montrera que le groupe fondamental d'une
variété abélienne est
isomorphe au
module de Tate complet(``full
Tate module'') |
| |
SM-038 |
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Cheng Yuan LU(Paris-13) |
19/12/2009 10h30 |
|
Simple modules of reductive groups |
2,3 of 3 |
| |
|
le
mémoire |
SM-037 |
|
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Yong Qi LIANG(Paris-11) |
05/12/2009 10h30 |
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Colliot-Thélène et la théorie de
Galois inverse |
1 de 1 |
|
Je voudrais expliquer pourquoi
une conjecture de Colliot-Thélène implique une
réponse affirmative du problème inverse de Galois
sur Q (ou un corps de nombres quelconque). |
| [1]Topics
in Galois theory par Serre.
[2]An effective version of
Hilbert's irreducibility theorem par Ekedahl |
SM-036 |
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Cheng Yuan LU(Paris-13) |
28/11/2009 14h30 |
|
Simple modules of reductive groups(mémoire
de M2 dirigé par Tilouine) |
1 of 3 |
| |
|
le
mémoire |
SM-035 |
|
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Peng SHAN(Paris-7) |
28/11/2009 10h30 |
|
La conjecture de Deligne-Langlands et algèbres
de Hecke affine |
1 de 1 |
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SM-034 |
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Chun Hui WANG(Paris-11) |
21/11/2009 14h30 |
|
Weil Representations |
2 of 2 |
| |
| |
SM-033 |
|
|
Chun Hui WANG(Paris-11) |
21/11/2009 10h30 |
|
Weil Representations |
1 of 2 |
| |
| |
SM-032 |
|
|
Yong HU |
14/11/2009 14h30 |
|
Groupe de Travail sur Groupes
Algébriques |
|
|
cf. GdT-GA01 |
|
Groupes Algébriques-M.Demazure,
P.Gabriel |
GdT-GA03 |
|
|
Marco MACULAN(Paris-11) |
14/11/2009 10h30 |
|
Théorie géométrique des invariants et majorations de
hauteurs |
2 de 2 |
|
cf. 1 de 2 |
| |
SM-031 |
|
|
Marco MACULAN(Paris-11) |
07/11/2009 10h30 |
|
Théorie géométrique des invariants et majorations de
hauteurs(mémoire
de M2 dirigé par Bost) |
1 de 2 |
|
L'exposés
se divisent en
trois parties: les
premières deux des rappels resp. sur la théorie
géométrique des invariants (quand même les
définitions, les théorèmes principaux et des
exemples) et sur les concepts fondamentaux de
la géométrie d'Arakelov (fibrés hermitiens,
et hauteurs "à la Arakelov" avec des exemples
concrets). La troisième partie sera sur la
minoration de hauteurs que présentée dans mon
mémoire: après avoir les
objets qui apparaissent, je voudrai donner la preuve
dans un des deux cas (géométrique ou arithmétique)
et, enfin, conclure en montrant comment
ce résultat peut être utilisé en géométrie
diophantienne. |
|
le mémoire |
SM-030 |
|
|
Yong HU |
31/10/2009 10h30 |
|
Groupe de Travail sur Groupes
Algébriques |
|
|
cf. GdT-GA01 |
|
Groupes Algébriques-M.Demazure,
P.Gabriel |
GdT-GA02 |
|
|
Arno KRET(Paris-11) |
24/10/2009 10h00 |
|
Modular forms from a moduli perspective |
3,4 of 4 |
|
3) Automorphic forms. Recall the definition of
cuspidal autom forms on GL_2. Make the passage from
modular forms (as explained in the previous chapter)
to automorphic forms, and state PRECISELY what the
relation is between the two. I will end with the
conclusion that the theorem of modularity implies
the global Langlands conjecture for the Galois
representations which occur in the Tate module of an
elliptic curve. (this chapter will take probably 2
talks) |
| cf.
1 of 4 |
SM-029 |
|
|
Yong HU |
17/10/2009 10h00 |
|
Groupe de Travail sur Groupes
Algébriques |
|
In the opening lectures of this GdT, I would like to give a quick but informative
introduction to the langue used in the book "Groupes Algebriques" (by Demazure and
Gabriel). The goal is to familiarize ourselves to the following notions/results:
k-functors (with k a ring), functors between k-functors and locally ringed spaces,
construction of grassmannians, local functors, open subfunctors, characterization of
functors representable by schemes (comparison theorem), extension and (Weil)
restriction of scalars.
|
|
Groupes Algébriques-M.Demazure,
P.Gabriel
notes |
GdT-GA01 |
|
|
Arno KRET(Paris-11) |
10/10/2009 14h00 |
|
Modular forms from a moduli perspective |
2 of 4 |
|
2) Modular forms. Introduce modular forms as
sections of the sheaf of relative differentials on
the universal elliptic curve. Move towards functions
of lattices, derive the classical formulas that
define modular forms as holomorphic functions on the
complex upper half plane satisfying certain
transformation rules w.r.t. a certain congruence
subgroup of SL_2(Z). |
| cf.
1 of 4 notes |
SM-028 |
|
|
Ting Yu LEE(Paris-6) |
10/10/2009 10h00 |
|
Flasque resolutions of algebraic tori |
1 of 1 |
|
sur le mémoire de M2 dirigé par
P.Gille, pour le résumé cf. le lien suivant. |
|
le mémoire |
SM-027 |
|
|
Arno KRET(Paris-11) |
03/10/2009 10h00 |
|
Modular forms from a moduli perspective |
1 of 4 |
Abstract: Classically modular forms are defined on
the complex half plane as functions satisfying
certain transformation properties. In this series of
these talks I will define modular forms as certain
sections of a certain line bundle on the universal
elliptic curve representing a certain moduli
problem. I will then move towards the classical
formulas which define modular forms.
The aim of these talks is to provide a more
conceptual understanding of what modular forms are,
rather than just giving a bunch of formulas that
define them.
1) Brief review of elliptic curves over arbitrary
base (no proofs here, only statements and defs).
(relatively) (representable) moduli problems,
geometric properties of moduli problems, examples
of moduli problems: the 4 basic moduli problems
and their properties of representability. (Coarse
moduli schemes, if time permits)
|
References: Talk notes of Edixhoven on GL_2 (part 3
is basically copied from his notes),
http://www.math.leidenuniv.nl/~edix/talks/2009_02_09/GL2.pdf and the
original handwritten notes,
http://www.math.leidenuniv.nl/~edix/talks/2009_02_09/GL2_handwritten.pdf.
Deligne, in SPM 349.
The book Katz Mazur, the Arithmetic moduli of
elliptic curves. Chapters 2 and 4.
Thesis of Johan Bosman,
http://www.uni-due.de/~ada649b.
Talk notes of Edixhoven for the course topic in
arithmetic geometry that he gave in Leiden sept '09,
http://www.math.leidenuniv.nl/~edix/tag_2009/tag1-2.html |
SM-026 |
|
|
|
|
|
|
| 2008-2009 |
|
|
|
Yih Dar SHIEH(Paris-11 ALGANT) |
28/06/2009(dimanche) 10h00 |
| |
1 of 1 |
|
I will sketch Bombieri's proof of Riemann
Hypothesis for algebraic curves, which used only
Riemann-Roch theorem and basic Galois Theory. In the
second part, I describe (two) applications of
Artin-Schreier extension to exponential sum and coding
theory. If possible, I will mention the relation of
exponential sum and factors of Jacobians. |
| |
SM-025 |
|
|
|
|
|
|
Wen Wei LI(Paris-7) |
16/05/2009 10h00 |
|
Un aperçu de la formule des traces d'Arthur-Selberg |
1 de ? |
La
formule des traces fut inventée par Selberg en 1956 pour
traiter questions arithmétiques liées au groupe SL(2). Une
généralisation à
groupes réductifs est obtenue par Arthur pendant 1974-2003.
Elle permet de déduire, par exemple, la correspondance de
Jacquet-Langlands, changement de base cyclique (apparu dans
la démonstration du théorème de modularité) et les résultats
récents sur
la conjecture de Sato-Tate. Soyons réalistes, nous nous
contenterons d'exposer les idées de base. |
| ref.
J. Arthur, An
Introduction to the Trace Formula S.
Gelbart, Lectures
on the Athur-Selgerg Trace Formula |
SM-022 |
|
|
Yong Qi LIANG(Paris-11) |
21/03/2009 14h15 |
|
Théorèmes de dualité en arithmétique
(suite) |
1 de 1 |
| Je
vais vous expliquer la dualité en arithmétique en terme de
la cohomologie étale (de Artin-Verdier), et TDA pour les
variétés algébriques sur un corps global, et finalement TDA
pour les 1-motives. |
| |
SM-021 |
|
|
Guo Dong ZHOU(Universität zu Köln - Allemagne) |
21/03/2009 10h00 |
|
Sur une conjecture d'Auslander and Reiten |
1 de 1 |
|
Une conjecture d'Auslander-Reiten dit que si les
categories stables de deux algebres de dimension finie
definies sur un corps algebriquement clos sont
equivalentes, alors ces deux algebres ont meme nombre des
classes d'isomorphismes des modules simples
non-projectifs. Dans cet expose, on s'interesse a cette
conjecture pour une equivalence stable de type de Morita
qui a ete introduite par Broue dans les annees 90. On
donnerai des conditions equivalentes de cette conjecture,
Le point critique est de definir une notion de l'homologie
de Hochschild stable de degre zero.
|
| |
SM-020 |
|
|
Yong Qi LIANG(Paris-11) |
14/03/2009 10h00 |
|
Quelques théorèmes de dualité en
arithmétique |
1 de 1 |
| Je
vais parler de l'histoire de théorèmes de dualité en
arithmétique. Les résultats principaux sur ce sujet seront
énoncés. Mais il n'y aura peu de preuves dans cet exposé. |
| le
mémoire |
SM-019 |
|
|
Arno KRET(Leiden University - The Netherlands) |
21/02/2009 10h00 |
|
The global Langlands conjecture |
2 of 2 |
| cf
1 of 2 |
| |
SM-018 |
|
|
Arno KRET(Leiden University - The Netherlands) |
14/02/2009 10h00 |
|
The global Langlands conjecture |
1 of 2 |
In
these two talks I will give a statement of the Langlands
conjecture for the field Q.
Let l be a prime number and A the ring of Q-adeles. The
Langlands conjecture sets up a bijection between
(isomorphism classes of) automorphic representations of
Gl_n(A) to geometric l-adic representations of the absolute
Galois group of Q, such that L-factors correspond to
L-factors.
The goal of my talk will be to explain all the words
occurring in the above phrase (except prime number, number
field and bijection maybe...). I try to be as easy and
precise as possible, after all it is Saturday. |
| |
SM-017 |
|
|
Alena PIRUTKA(Paris-11) |
13/12/2008 10h00 |
|
Etude de la $R$-équivalence sur des variétés
rationnellement connexes |
3 de 3 |
| cf.
1 de 3 |
| le
texte |
SM-016 |
|
|
Alena PIRUTKA(Paris-11) |
06/12/2008 10h00 |
|
Etude de la $R$-équivalence sur des variétés
rationnellement connexes |
2 de 3 |
| cf.
1 de 3 |
| |
SM-015 |
|
|
Xu SHEN(Paris-11 ALGANT M2) |
29/11/2008 14h15 |
|
On Deligne-Lusztig theory and non-abelian Lubin-Tate theory |
2 of 2 |
| cf.
1 of 2 |
| |
SM-014 |
|
|
Alena PIRUTKA(Paris-11) |
29/11/2008 10h00 |
|
Etude de la $R$-équivalence sur des variétés
rationnellement connexes |
1 de 3 |
| résumé |
| |
SM-013 |
|
|
Giovanni Di Matteo |
22/11/2008 14h15 |
|
Les bornés de Serre pour GL_n(k) |
2 of 4 |
| cf.
SM-003 |
| |
SM-012 |
|
|
Xu SHEN(Paris-11 ALGANT M2) |
22/11/2008 10h00 |
|
On Deligne-Lusztig theory and non-abelian Lubin-Tate theory |
1 of 2 |
| In
this talk, we shall first review the classical
Deligne-Lusztig theory, which gives all the irreducible
representions of the reductive groups over finite
fields, by the l-adic cohomology with compact support
of certain smooth algebraic varieties ( Deligne-Lusztig
varieties ) over the algebraic closure of the finite field.
Then we turn to the calculation of the vanishing cycle
cohomology of the Lubin-Tate deformation space in the depth
0 case. Following Yoshida, we will construct some suitable
models of this moduli space by some
successive blowing-ups and normalization. We will at
last reduce to the calculation of the cohomology of the
Deligne-Lusztig variety contained as a special fibre in a
model constructed above, and thus obtain a purely local
proof of the result asserted by Harris-Taylor in this
special case. |
| |
SM-011 |
|
|
Ramla ABDELLATIF(Paris-11) |
15/11/2008
10h00 |
|
Représentations
modulo p de GL_2(F) III : Second construction de Paskunas
- Perspectives |
3 de 3 |
| Résumé
/ Abstract |
| |
SM-010 |
|
|
Ramla ABDELLATIF(Paris-11) |
08/11/2008
10h00 |
|
Représentations
modulo p de GL_2(F) II : Le cas de Q_p (2-ième partie) -
Première construction de Paskunas |
2 de 3 |
| Résumé
/ Abstract |
| |
SM-009 |
|
|
Yong HU(Paris-11) |
25/10/2008
14h15 |
R-equivalence and 0-cycles on 3-dim. tori II
: K-theory of toric models and the proof of Merkerjev's
theorem |
2 of 2 |
| cf.
SM-005 |
Main references:
[1] J.-L. Colliot-Thelene, J.-J. Sansuc, "La R-equivalence
sur les tores", Ann. Sci. Ecole
Norm. Sup. (4) 10 (1977), 1755–229.
[2] W. Fulton, "Intersection theory", 2nd ed.,
Springerr–Verlag, 1998.
[3] A. Merkurjev, "R-equivalence on 3-dimensional tori and
zero-cycles", Algebra and Number
Theory, to appear,
http://www.math.ucla.edu/~merkurev/publicat.htm
[4] D. Quillen, "Higher algebraic K -theory I", in LNM. 341,
Algebraic K -theory I,
Springer-Verlag (1973), 855–147. |
SM-008 |
|
|
Ramla ABDELLATIF(Paris-11) |
25/10/2008 10h00 |
|
Représentations
modulo p de GL_2(F) I : Présentation générale - le cas de
Q_p (1-ière partie) |
1 de 3 |
| Résumé
/ Abstract |
| le
mémoire |
SM-007 |
|
|
Wen-Wei LI(Paris-7) |
18/10/2008 14h15 |
|
La représentation de Weil et son
caractère |
3 de 3 |
| On
introduira des notions fondamentales du groupe metapléctique
et représentation de Weil. On en parlera aussi l'analyse
harmonique et des applications arithmétiques. |
|
le mémoire |
SM-006 |
|
|
Yong HU(Paris-11) |
18/10/2008 10h00 |
|
R-equivalence and 0-cycles on 3-dim. tori I : Chow groups
with the link to K-theory, and R-equivalence on tori |
1 of 2 |
This
seris of talks, based on my master thesis done at
Leiden,aims to explain the following theorem recently proved
by A.Merkerjev:
Theorem: Let T be an algebraic torus over a field k,and let
X be a smooth compactification of T. Suppose dim T\le 3.
Then the map:
\phi: T(k)/R \rightarrow A_0(X); t\mapsto
[t]-[1] is an isomorphism of groups, where
T(k)/R is the group of R-equivalence classes on the rational
points of T and A_0(X) is the group of 0-cycle classes of
degree 0 on X.
Although the result obtained is not of too much generality,
this theorem is beautiful in my view, because it has made
connections
between many interesting arithmetic or algebro-geometric
objects. To these objects, I'll try to give a brief
introduction with an effort
to minimize the set of abstract definitions in need. After
that, the talk will be focused on ideas about how the
knowledge of these objects helps to prove the main theorem.
|
|
le mémoire |
SM-005 |
|
|
Wen-Wei LI(Paris-7) |
11/10/2008 14h00 |
|
La représentation de Weil et son
caractère |
2 de 3 |
| On
introduira des notions fondamentales du groupe metapléctique
et représentation de Weil. On en parlera aussi l'analyse
harmonique et des applications arithmétiques. |
|
le mémoire |
SM-004 |
|
|
Giovanni Di Matteo |
11/10/2008 10h00 |
|
The algebraic fundamental group,
Cebotarev's density theorem, and the foundations of
étale cohomology |
1 of 4 |
| Abstract |
| |
SM-003 |
|
|
Chun Hui WANG(Paris-11) |
04/10/2008 14h30 |
|
Rationality of the zeta function
of algebraic variety |
1 of 1 |
|
For higher dimensional varieties,the rationality of the zeta
function and the functional equation were first
proved by Dwork in 1960,using the
methods of p-adic analysis.It is an important event in
the struggling process for the Weil conjecture. On
this petite report, I will try to
recover the mostly part of the proof. |
| |
SM-002 |
|
|
Wen-Wei LI(Paris-7) |
04/10/2008 10h00 |
|
La représentation de Weil et son
caractère |
1 de 3 |
|
On introduira des notions fondamentales du groupe
metapléctique et représentation de Weil. On en parlera aussi
l'analyse harmonique et des applications arithmétiques. |
|
le mémoire |
SM-001 |
|
| |
|
| |
|