On the 'main conjecture' of equivariant Iwasawa theory

TL;DR

This paper proves the main conjecture of equivariant Iwasawa theory for totally real number field extensions at odd primes, assuming the vanishing of the Iwasawa - invariant, confirming key theoretical predictions.

Contribution

It establishes the main conjecture in equivariant Iwasawa theory under the assumption of - invariant vanishing for arbitrary totally real extensions.

Findings

Main conjecture proven at odd primes

Results depend on - invariant vanishing assumption

Extends previous results to arbitrary totally real extensions

Abstract

Assuming that Iwasawa's $\mu_{K/k}$-invariant vanishes, we prove the 'main conjecture' of equivariant Iwasawa theory, at odd prime numbers $l$, for arbitrary extensions $K/k$ of totally real number fields, up to its uniqueness assertion.