The Iwasawa Main conjecture of constant ordinary abelian varieties over function fields

TL;DR

This paper investigates a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over certain function field extensions, extending understanding of their arithmetic properties in a geometric context.

Contribution

It introduces a geometric analogue of the Iwasawa Main Conjecture specifically for constant ordinary abelian varieties over $bZ_p^d$-extensions of function fields.

Findings

Establishes a version of the Iwasawa Main Conjecture in a geometric setting.

Analyzes ramification at finite sets of places in the context of function fields.

Provides new insights into the arithmetic of abelian varieties over function field extensions.

Abstract

We study a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over $\ZZ_p^d$-extensions of function fields ramifying at a finite set of places.