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

## Arithmetic Algebraic Geometry LectureiWuj

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## Arithmetic Algebraic Geometry Lecture (Intensive Lecture Course)

 Dates: (4 lectures) October 10 (Tue) 13:30-15:00 15:15-16:45 October 13 (Fri) 13:30-15:00 15:15-16:45 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 (16:00-17:00) Speaker: Ambrus Pál (Imperial College, London) Title: Drinfeld modular curves and the arithmetic of elliptic curves over global function fields Abstract: 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. (17:15-18:15) Speaker: Chia-Fu Yu (Academia Sinica) Title: The supersingular loci and mass formulas on Siegel modular varieties Abstract: 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.