## 代数学コロキウム

開催情報 水曜日　17:00～18:00　数理科学研究科棟(駒場) 056号室 今井 直毅, 三枝 洋一

### 2008年07月16日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
On p-adic differential equation on semi-stable varieties

### 2008年07月02日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

(安田正大氏との共同研究)

### 2008年06月18日(水)

16:30-18:45   数理科学研究科棟(駒場) 117号室

On a ramification bound of semi-stable torsion representations over a local field

Beilinson-Tate予想と楕円曲面のK_1の不分解元
[ 講演概要 ]
(佐藤周友氏との共同研究)

これは、p進レギュレーターの非消滅と関係しており、

### 2008年06月04日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)

[ 講演概要 ]
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and

### 2008年05月07日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

(東京大学大学院数理科学研究科)
On the connected components of moduli spaces of finite flat models

### 2008年04月30日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
[ 講演概要 ]
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.

### 2008年01月30日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Luc Illusie 氏 (Universite Paris-Sud 11)
Odds and ends on finite group actions and traces
[ 講演概要 ]
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.

### 2008年01月23日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Weizhe Zheng 氏 (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
[ 講演概要 ]
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.

### 2008年01月16日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
[ 講演概要 ]
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.

### 2007年12月05日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

Classification of two dimensional trianguline representations of p-adic fields
[ 講演概要 ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).

### 2007年11月21日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Christopher Rasmussen 氏 (京都大学数理解析研究所)
Abelian varieties with constrained torsion
[ 講演概要 ]
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.

### 2007年10月31日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)

### 2007年10月24日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
[ 講演概要 ]

### 2007年10月10日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

James Lewis 氏 (University of Alberta)
Abel-Jacobi Maps Associated to Algebraic Cycles I

[ 講演概要 ]
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.

### 2007年09月19日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Gereon Quick 氏 (Universitaet Muenster)
Etale cobordism
[ 講演概要 ]
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.

### 2007年09月12日(水)

15:00-18:00   数理科学研究科棟(駒場) 117号室

E. Lau 氏 (Univ. of Bielefeld) 15:00-15:45
Classification of p-divisible groups by displays and duality
T. Zink 氏 (Univ. of Bielefeld) 16:00-16:45
Applications of the theory of displays
E. Looijenga 氏 (Univ. of Utrecht) 17:00-18:00
Presentation of mapping class groups from algebraic geometry
[ 講演概要 ]
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.

### 2007年08月27日(月)

16:30-17:30   数理科学研究科棟(駒場) 002号室
Steven Zucker 氏 (Johns Hopkins大学)
The reductive Borel-Serre motive

### 2007年07月18日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

Tropical toric varieties

### 2007年07月11日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Andreas Rosenschon 氏 (University of Alberta)
Algebraic cycles on products of elliptic curves over p-adic fields

### 2007年06月27日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室
Stephen Lichtenbaum 氏 (Brown University)
The conjecture of Birch and Swinnerton-Dyer is misleading
[ 講演概要 ]
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.

### 2007年05月09日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

$(g,K)$-module structures of principal series representations
of $Sp(3,R)$

### 2007年05月02日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields

### 2007年04月25日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

Localized Characteristic Class and Swan Class

### 2007年04月11日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

l進層の暴分岐と特性サイクル

### 2007年01月31日(水)

15:15-18:45   数理科学研究科棟(駒場) 117号室
3講演です

Dennis Eriksson 氏 (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 氏 (Utrecht) 17:45-18:45
Irreducibility of strata and leaves in the moduli space of abelian varieties