MS Seminar (Mathematics - String Theory)

Speaker: Yuken Miyasaka (Tohoku U)
Title: Torsion points on Jacobian varieties and p-adic Sato theory
Date (JST): Tue, Jul 03, 2012, 13:15 - 14:45
Place: Seminar Room A
Abstract: The classical Sato theory describes solutions of complete integrable equations in terms of Sato tau-functions. Anderson developed a p-adic theory of Sato tau-functions and applied it to arithmetic problem about torsion points on Jacobian varieties. He proved that torsion points of certain prime orders are not on the theta divisor of the Jacobian variety of X, where X is a cyclic quotient of a Fermat curve of prime degree. In this talk, I will report a work with Takao Yamazaki about an analogous result when X is a hyperelliptic curve. Recently, Kobayashi and Yamazaki proved for more general curves. These proofs are based on the "p-adic Sato theory".