p-adic Sato theory and arithmetic geometry

为了阐明非线性偏微分方程（如KdV和KP方程）的可积结构，Mikio Sato引入了tau函数。安德森引入了它的p-adic类似物并将其应用于算术问题：雅可比簇的theta因子上很少存在“素数阶”的扭点。我们把这个结果推广到“素幂序”。在证明这一结果的过程中，我们建立了许多关于p-adic Sato理论的基础性结果，这些结果对以后的其他研究也是有用的。

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.