RIMS International Project Research 2006 ``Arithmetic Algebraic Geometry''
  Arithmetic Algebraic Geometry Seminars & Lectures  

Arithmetic Algebraic Geometry Lecture

Place: 数理研202号室
Speaker: 辻雄(東大・数理/京大・数理研)
Title: p進Hodge理論の概説
Abstract: p進表現論の基礎とその最近の進展について 紹介した後、p進コホモロジーの比較定理、Variations、 基本群のp進Hodge理論について解説する。

Arithmetic Algebraic Geometry Lecture
(Intensive Lecture Course)

Dates: (4 lectures)
October 10 (Tue) 13:30-15:00
October 13 (Fri) 13:30-15:00
Place: Room 202, RIMS
Speaker: Minhyong Kim (Purdue Univ./RIMS, Kyoto Univ.)
Title: Path spaces and Diophantine geometry
Abstract: We will explain how integral points on hyperbolic curves can be controlled using torsors of paths for unipotent fundamental groups.

Arithmetic Algebraic Geometry Seminar

Date: September 13 (Wed), 2006, 16:00-18:30
Place: Room 420, RIMS

Speaker: Ambrus Pál (Imperial College, London)
Title: Drinfeld modular curves and the arithmetic of elliptic curves over global function fields   
Drinfeld modular curves are global function field analogues of elliptic modular curves. One reason for their study is that they parameterize elliptic curves defined over global function fields, similarly to the classical situation. I will talk about how one may use such a modular parameterization to prove relations between rigid-analytic periods of objects of diophantine interest living on elliptic curves and special values of L-functions.

Speaker: Chia-Fu Yu (Academia Sinica)
Title: The supersingular loci and mass formulas on Siegel modular varieties   
In this talk we will describe the results of Katsura and Oort on the supersingular locus of the Siegel 3-folds. Then we state the mass formula for superspecial principally polarized abelian varieties due to Ekedahl and some others. We extend the work of Katsura and Oort to the space with a parahoric level and the work of Li and Oort the irreducible components of the supersingular locus of the Siegel modular varieties.

Arithmetic Algebraic Geometry Lecture
Dates: (全5回)
7月10日(月) 16:30-18:00
  11日(火) 16:30-18:00
  12日(水) 17:30-19:00(時間注意)
  13日(木) 16:30-18:00
  14日(金) 14:45-16:15(時間注意)
Place: 数理研115号室
Speaker: 花村昌樹(東北大・理/京大・数理研)
Title: モティーフ理論の応用を主とした解説
Abstract: モティーフを聞いたことはない人に対し,混合モティーフの圏の性質,モティーフ層 の圏の性質を述べ(使う人の立場を考え,圏の構成などには深く立ち入らない), その応用をいくつかのべる.話題としては,(1) 多重ゼータ値の次元の評価 (Goncharov, Terasoma), および(2) ファイバー多様体(とくにモジュラー多様体) のモティーフ分解を考えている.

Arithmetic Algebraic Geometry Seminar
Date: June 2 (Fri), 2006, 16:30-17:30
Place: Room 202, RIMS
Speaker: Christopher Rasmussen (Rice Univ.)
Title: Arithmetic from Geometry on Elliptic Curves   
Abstract:   [pdf]
One of the philosophies of arithmetic geometry made popular by Grothendieck was the notion that the structure of the absolute Galois group of $\mathbf{Q}$, could be determined from geometric (or even combinatoric) data. In a related vein, one finds that the arithmetic properties of a curve are sometimes determined by its geometry. Specifically, the structure of a curve as a cover of the projective line can have arithmetic consequences for the Jacobian of the curve. We will discuss this situation in the case of elliptic curves, where this connection between arithmetic and geometry can be seen very clearly.

Arithmetic Algebraic Geometry Lecture
Dates & Places: (全9回)
5月 8日(月) 17:00-18:30  数理研115号室
   9日(火) 17:00-18:30  数理研115号室
  10日(水) 17:30-19:00  数理研115号室 (時間注意)
  11日(木) 17:00-18:30  数理研420号室 (場所注意)
  12日(金) 17:00-18:30  数理研115号室
  15日(月) 17:30-19:00  数理研115号室(時間注意)
  16日(火) 17:30-19:00  数理研115号室(時間注意)
  17日(水) 17:30-19:00  数理研420号室(時間・場所注意)
  19日(金) 17:00-18:30  数理研115号室
Speaker: 加藤和也(京大・理)
Title: Weil 予想とエタールコホモロジー
Abstract: Weil が 1949 年に提出した Weil 予想は、 1970 年代のはじめに最終的に証明されるまで、 代数幾何学の大きな進展の原動力となり、 とくに Grothendieck が Weil 予想の証明をめざして導入したエタールコホモロジーは、 現在の整数論の重要な道具となった。 その経緯をふり返りつつ、エタールコホモロジーの解説をおこなう。

Arithmetic Algebraic Geometry Seminar
Date: May 1 (Mon), 2006, 16:30-
Place: Room 202, RIMS
Speaker: Lucien Szpiro (City Univ. New York)
Title: Algebraic dynamical systems (preperiodic points, Mahler measures, equidistribution of small points)
Reference: (available at http://math.gc.cuny.edu/faculty/szpiro/People_Faculty_Szpiro.html)
--Joint papers with T. Tucker
--Joint paper with E. Ullmo and S. Zhang

Date:   April 10 (Mon), 2006, 14:00-17:00
Place:   Room 202, RIMS

Speaker: Michel Matignon (Univ. Bordeaux 1/Chuo Univ.)
Title: Wild monodromy groups and automorphisms groups of curves

Speaker: Barry Green (Univ. Stellenbosch/Chuo Univ.)
Title: Selected results on liftings of Galois covers of smooth curves
from char. p to char. 0

Organizing Committee
Kazuya Kato (Kyoto University)
Hiroyuki Yoshida (Kyoto University)
Atsushi Moriwaki (Kyoto University)
Akio Tamagawa (RIMS, Kyoto University)
Shinichi Mochizuki (RIMS, Kyoto University)


Research Institute for Mathematical Sciences