Adams operations and Galois structure

Pappas, Georgios

doi:10.2140/ant.2015.9.1477

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Adams operations and Galois structure

Georgios Pappas

Vol. 9 (2015), No. 6, 1477–1514

DOI: 10.2140/ant.2015.9.1477

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

Vol. 9, No. 6, 2015