The Iwasawa main conjecture for semistable abelian varieties over function fields

TL;DR

This paper proves the Iwasawa main conjecture for semistable abelian varieties over function fields in characteristic p, extending the understanding of Iwasawa theory in positive characteristic.

Contribution

It establishes the Iwasawa main conjecture for semistable abelian varieties over function fields in characteristic p, a significant advancement in arithmetic geometry.

Findings

Proves the Iwasawa main conjecture in the specified setting.

Extends Iwasawa theory to positive characteristic function fields.

Provides new tools for studying abelian varieties over function fields.

Abstract

We prove the Iwasawa main conjecture over the arithmetic $\mathbb{Z}_p$-extension for semistable abelian varieties over function fields of characteristic $p>0$.