Picard 1-motives and Tate sequences for function fields

Abstract

We use our previous work [4] on the Galois module structure of `–adic realizations of Picard 1–motives to construct explicit representatives in the `–adified Tate class (i.e. explicit `–adic Tate sequences, as defined in [8]) for general Galois extensions of characteristic p > 0 global fields. If combined with the Equivariant Main Conjecture proved in [4], these results lead to a very direct proof of the Equivariant Tamagawa Number Conjecture for characteristic p > 0 Artin motives with abelian coefficients.