On the Tate-Shafarevich group of Abelian schemes over higher dimensional bases over finite fields

TL;DR

This paper investigates the properties of the Tate-Shafarevich group for Abelian schemes with good reduction over higher dimensional bases defined over finite fields, extending classical theories to more complex geometric settings.

Contribution

It introduces new analogues of the Tate-Shafarevich group in the context of higher dimensional bases over finite fields, expanding understanding beyond traditional one-dimensional cases.

Findings

Established properties of the Tate-Shafarevich group in higher dimensions

Extended classical results to new geometric contexts

Provided foundational results for future research in arithmetic geometry

Abstract

We study analogues for the Tate-Shafarevich group for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields.