Verifying a p-adic abelian Stark conjecture at s=1

Integral and p-adic Refinements of the Abelian Stark Conjecture

We give a formulation of the abelian case of Stark’s Main Conjecture in terms of determinants of projective modules and briefly show how this formulation leads naturally to its Equivariant Tamagawa Number Conjecture (ETNC) – type integral refinements. We discuss the Rubin-Stark integral refinement of an idempotent p1 iece of Stark’s Abelian Main Conjecture. In the process, we give a new formula...

ON THE p-ADIC STARK CONJECTURE AT s = 1 AND APPLICATIONS

Let E/F be a finite Galois extension of totally real number fields and let p be a prime. The ‘p-adic Stark conjecture at s = 1’ relates the leading terms at s = 1 of p-adic Artin L-functions to those of the complex Artin L-functions attached to E/F . We prove this conjecture unconditionally when E/Q is abelian. Moreover, we also show that for certain non-abelian extensions E/F the p-adic Stark ...

On the Non-abelian Brumer–stark Conjecture

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer–Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa μ-invariant. In combination with the authors’ previous work on the EIMC, this leads to uncond...

The Rank One Abelian Stark Conjecture

THE SEGAL CONJECTURE FOR ELEMENTARY ABELIAN p-GROUPS-II. p-ADIC COMPLETION IN EQUIVARIANT COHOMOLOGY

This result implies an analogue for general finite groups, but we refer the reader to [25] and especially [S] for that. We shall give as efficient a proof of the theorem as present technology seems to allow, starting from the purely algebraic Ext calculation [4,1.1] of Adams, Gunawardena, and Miller as a given. When G=(Zp)‘, the theorem is due to those authors. However, their original passage f...