An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications
Abstract
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- American Journal of Mathematics
- Publisher
- Project MUSE
- Volume
- 148
- Issue
- 2
- Pages
- 389–442
- Publication date
- 31 March 2026
- Language
- EN