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Nearly Perfect Complexes and Galois Module Structure

Published online by Cambridge University Press:  04 December 2007

T. CHINBURG ,
M. KOLSTER ,
G. PAPPAS  and
V. SNAITH
T. CHINBURG
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA. 19104, U.S.A. e-mail: ted@math.upenn.edu
M. KOLSTER
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L86 4K1. e-mail: kolster@mcmail.cis.McMaster.ca
G. PAPPAS
Affiliation:
Department of Mathematics, Michigan State Univ., Wells Hall, East Lansing, MI 48824, U.S.A. e-mail: pappas@math.msu.edu
V. SNAITH
Affiliation:
Department of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ United Kingdom. e-mail: vps@maths.soton.ac.uk
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Abstract

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We define a generalization of the Euler characteristic of a perfect complex of modules for the group ring of a finite group. This is combined with work of Lichtenbaum and Saito to define an equivariant Euler characteristic for G on regular projective surfaces over Z having a free action of a finite group. In positive characteristic we relate the Euler characteristic of G to the leading terms of the expansions of L-functions at s=1.

Keywords

Galois structureEuler characteristicssurfaceL-function.
Type
Research Article
Information
Compositio Mathematica , Volume 119 , Issue 2 , November 1999 , pp. 133 - 155
Copyright
© 1999 Kluwer Academic Publishers