Adams operations and Galois structure

Abstract

We present a new method for determining the Galois module structure of the cohomology of coherent sheaves on varieties over the integers with a tame action of a finite group. This uses a novel Adams–Riemann–Roch-type theorem obtained by combining the Künneth formula with localization in equivariant $K$-theory and classical results about cyclotomic fields. As an application, we show two conjectures of Chinburg, Pappas, and Taylor in the case of curves.