Equivariant Iwasawa theory and non-abelian Stark-type conjectures

Abstract

We discuss three different formulations of the equivariant Iwasawa main conjecture attached to an extension K/k of totally real fields with Galois group G, where k is a number field and G is a p-adic Lie group of dimension 1 for an odd prime p. All these formulations are equivalent and hold if Iwasawa's μ-invariant vanishes. Under mild hypotheses, we use this to prove non-abelian generalizations of Brumer's conjecture, the Brumer-Stark conjecture and a strong version of the Coates-Sinnott conjecture provided that μ= 0.

29 pages, minor changes, to appear in Proc. Lond. Math. Soc

References in corpus (2)

• The main conjecture of Iwasawa theory for totally real fields
• An Equivariant Main Conjecture in Iwasawa Theory and Applications

Cited by in corpus (3)

• Noncommutative Fitting invariants and improved annihilation results
• Fitting invariants in equivariant Iwasawa theory
• On the p-adic Stark conjecture at s=1 and applications