p-adic Sato theory and arithmetic geometry

点击翻译按钮获取中文摘要

In order to clarify the integrable structure of non-linear PDEs such as KdV and KP equations, Mikio Sato introduced the tau function. Anderson introduced its p-adic analogue and applied it to arithmetic problem : a torsion point of"prime order" on the theta divisor of a Jacobian variety seldom exists. We extended this result to"prime power order". In the course of proving this result, we established many fundamental results on p-adic Sato theory, which are expected to be useful for other future research as well.