Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture

TL;DR

This paper proves the equivariant Iwasawa main conjecture for certain non-abelian p-adic Lie extensions of totally real fields without assuming mu-invariant vanishing, advancing understanding in algebraic number theory.

Contribution

It provides an unconditional proof of the conjecture for a broad class of extensions, independent of mu-invariant assumptions.

Findings

Unconditional proof of the conjecture for specific non-abelian extensions

Extension of the conjecture's validity beyond mu-invariant vanishing cases

Progress in understanding Iwasawa theory for non-abelian p-adic Lie extensions

Abstract

Let p be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for an infinite class of one-dimensional non-abelian p-adic Lie extensions. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant.