## Number Theory Seminar

Date, time & place Wednesday 17:00 - 18:00 056Room #056 (Graduate School of Math. Sci. Bldg.) Naoki Imai, Yoichi Mieda

Seminar information archive

### 2007/01/31

15:15-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Dennis Eriksson (東大数理/Paris) 15:15-16:15
Towards a proof of a metrized Deligne-Riemann-Roch theorem

CM楕円曲線の超特異点における2変数p進L関数
(A two variable p-adic L-function for CM elliptic curves at supersingular primes)
Frans Oort (Utrecht) 17:45-18:45
Irreducibility of strata and leaves in the moduli space of abelian varieties

### 2006/12/20

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
On the profinite regular inverse Galois problem
[ Abstract ]
Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \\textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\\\\
\\indent Let $p\\geq 2$ be a prime, then a profinite group
$G$ is said to be \\textit{$p$-obstructed} if it fits in a profinite group extension
$$1\\rightarrow K\\rightarrow G\\rightarrow G_{0}\\rightarrow 1$$
with $G_{0}$ a finite group and $K\\twoheadrightarrow \\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\\\\
\\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \\textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\\not= p$.\\\\
\\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\\rightarrow X_{G})_{n\\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
Eric Friedlander (Northwestern) 17:45-18:45
An elementary perspective on modular representation theory

### 2006/12/06

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Vincent Maillot (Jussieu/京大数理研) 16:30-17:30
New applications of the arithmetic Riemann-Roch theorem
Don Blasius (UCLA) 17:45-18:45
Zariski Closures of Automorphic Galois Representations

### 2006/11/01

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
G.Bayarmagnai (東大数理) 16:30-17:30
Essential dimension of some finite group schemes
Jacques Tilouine (パリ北大学) 17:45-18:45
Overconvergent Siegel modular forms
[ Abstract ]
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.

### 2006/10/25

17:00-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)

Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )
[ Abstract ]

### 2006/10/18

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Fabrice Orgogozo (東大数理・Ecole Polytechnique de Paris) 16:30-17:30
p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique
Kim Minhyong (Purdue大学・京大数理研) 17:45-18:45
Fundamental groups and Diophantine geometry

### 2006/09/06

16:30-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Bas Edixhoven (Univ. of Leiden)
Computation of the mod l Galois representations associated to Delta

### 2006/08/25

16:30-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
A. Marmora (パリ北大・東大/学振)

### 2006/07/12

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Beilinson-Drinfeld chiral algebra, geometric Langlands program and open Gromov-Witten invariants
[ Abstract ]

### 2006/06/28

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Configuration of the central streams in the moduli of abelian varieties

### 2006/06/07

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Hecke-Siegel's pull back formula for the Epstein zeta function with spherical

### 2006/05/24

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Kai Köehler (Düesseldorf 大学) 16:30-17:30
Quaternionic analytic torsion and arithmetic geometry
Thomas Geisser (南カリフォルニア大学) 17:45-18:45
Duality via cycle complexes

### 2006/04/26

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Differential Operators of Rankin-Cohen-Ibukiyama Type for Automorphic Forms of Several Variables

### 2006/04/19

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Distributions of discriminants of cubic algebras