$\ell$-adic Tautological Systems

TL;DR

This paper introduces $$-adic tautological systems, extending the concept of tautological systems from complex geometry to positive characteristic fields, specifically characteristic p.

Contribution

The paper develops the theory of $$-adic tautological systems, adapting the framework of tautological systems to algebraic varieties over fields of characteristic p.

Findings

Defined $$-adic tautological systems in characteristic p

Extended the theory of period integrals to positive characteristic

Laid groundwork for further research in $$-adic geometry

Abstract

Tautological systems was introduced in Lian-Yau as the system of differential equations satisfied by period integrals of hyperplane sections of some complex projective homogenous varieties. We introduce the $\ell$-adic tautological systems for the case where the ground field is of characteristic $p$.