Andreas Nickel will speak on

The p-adic Stark conjecture and applications

Abstract: Let L/K be a Galois extension of totally real fields and let p be a prime. The p-adic Stark conjecture relates the leading terms at s = 1 of p-adic Artin L-functions to those of the complex Artin L-functions attached to L/K. When L=K this is equivalent to Leopoldt’s conjecture for L at p and the ‘p-adic class number formula’ of Colmez.

In this talk we discuss the p-adic Stark conjecture and (if time permits) new applications to the equivariant Tamagawa number conjecture. This is joint work with Henri Johnston (Exeter).