Vol. 9, No. 6, 2015

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Georgios Pappas

Vol. 9 (2015), No. 6, 1477–1514
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.

Keywords
Galois cover, Galois module, Riemann–Roch theorem, Euler characteristic
Mathematical Subject Classification 2010
Primary: 14L30, 14C40, 11S23
Secondary: 20C10, 14C35, 19E08, 11R33, 14F05