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

2020/10/06 by Henri Johnston, Johnston, Henri, Andreas Nickel +1
Mathematics · #11R23 #11R42 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.03186

openalex publication_date 2020/10/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime. We give an unconditional proof of the equivariant\nIwasawa main conjecture for totally real fields for every admissible\none-dimensional p-adic Lie extension whose Galois group has an abelian Sylow\np-subgroup. Crucially, this result does not depend on the vanishing of any\n\μ-invariant. As applications, we deduce the Coates-Sinnott conjecture away\nfrom its 2-primary part and new cases of the equivariant Tamagawa number\nconjecture for Tate motives.\n

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