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arXiv · 2010.03186

An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications

Henri Johnston·Andreas Nickel
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Abstract

Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois group has an abelian Sylow $p$-subgroup. Crucially, this result does not depend on the vanishing of any $\mu$-invariant. As applications, we deduce the Coates-Sinnott conjecture away from its $2$-primary part and new cases of the equivariant Tamagawa number conjecture for Tate motives.

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Henri Johnston, Andreas Nickel. 2020-10-06. An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications. https://arxiv.org/abs/2010.03186

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