The local equivariant Tamagawa number conjecture for almost abelian extensions

TL;DR

This paper proves the local equivariant Tamagawa number conjecture for motives associated with almost abelian extensions of imaginary quadratic fields, covering all split primes p ≠ 2, 3, at negative integer values s.

Contribution

It establishes the conjecture for a broad class of motives related to almost abelian extensions, extending previous results to all split primes p ≠ 2, 3.

Findings

Proves the conjecture for all split primes p ≠ 2, 3.

Validates the conjecture at all negative integer values s.

Advances understanding of Tamagawa number conjectures in number theory.

Abstract

We prove the local equivariant Tamagawa number conjecture for the motive of an abelian extension of an imaginary quadratic field with the action of the Galois group ring for all split primes p not equal to 2 or 3 at all negative integer values s.