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arXiv · 1109.5525

Equivariant Iwasawa theory and non-abelian Stark-type conjectures

Andreas Nickel
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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.

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Andreas Nickel. 2012-10-16. Equivariant Iwasawa theory and non-abelian Stark-type conjectures. https://doi.org/10.1112/plms%2Fpds086

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