On a noncommutative Iwasawa main conjecture for varieties over finite fields

TL;DR

This paper formulates and proves a noncommutative Iwasawa main conjecture analogue for l-adic Lie extensions of schemes over finite fields, extending prior number field results to algebraic geometry contexts.

Contribution

It introduces a new noncommutative Iwasawa main conjecture for schemes over finite fields and provides a proof, bridging number theory and algebraic geometry.

Findings

Established the conjecture for specific classes of schemes

Extended noncommutative Iwasawa theory to algebraic geometry

Provided new tools for studying l-adic Lie extensions

Abstract

In 2005 Coates, Fukaya, Kato, Sujatha, and Venjakob formulated a noncommutative Iwasawa main conjecture for l-adic Lie extensions of number fields. To provide evidence for this main conjecture we formulate and prove an analogous statement for l-adic Lie extensions of separated schemes of finite type over a finite field of characteristic prime to l.