On the Rubin?Stark Conjecture for a special class of CM extensions of totally real number fields

Abstract

We use Greither’s recent results on Brumer’s Conjecture to prove Rubin’s integral version of Stark’s Conjecture, up to a power of 2, for an infinite class of CM extensions of totally real number fields, called “nice extensions” under the assumption that a certain Iwasawa μ–invariant vanishes. As a consequence and under the same assumption, we show that the Brumer–Stark Conjecture is true for “nice extensions”, up to a power of 2.