Equivariant Iwasawa theory and non-abelian Stark-type conjectures

Details Equivariant Iwasawa theory and non-abelian Stark-type conjectures Equivariant Iwasawa theory and non-abelian Stark-type conjectures

2011-09-26

arxiv.org/abs/1109.5525v1

Mathematics

Number Theory

29 pages

Scientific paper

We discuss three different formulations of the equivariant Iwasawa main conjecture attached to an extension $\mc K/k$ of totally real fields with Galois group $\mc G$, where $k$ is a number field and $\mc G$ is a $p$-adic Lie group of dimension 1 for an odd prime $p$. All these formulations are equivalent and hold if Iwasawa's $\mu$-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 $\mu = 0$.

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