#### Vol. 9, No. 6, 2015

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Adams operations and Galois structure

### 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
##### Milestones
Received: 24 February 2015
Accepted: 27 March 2015
Published: 7 September 2015
##### Authors
 Georgios Pappas Department of Mathematics Michigan State University Wells Hall East Lansing, MI 48824-1027 United States