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Galois Module Structure and the γ-Filtration

Published online by Cambridge University Press:  04 December 2007

Georgios Pappas
Affiliation:
Department of Mathemathics, Wells Hall, Michigan State University, East Lansing, MI 48824, U.S.A. E-mail: [email protected]
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Abstract

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We describe a general method for calculating equivariant Euler characteristics. The method exploits the fact that the γ-filtration on the Grothendieck group of vector bundles on a Noetherian quasi-projective scheme has finite length; it allows us to capture torsion information which is usually ignored by equivariant Riemann–Roch theorems. As applications, we study the G-module structure of the coherent cohomology of schemes with a free action by a finite group G and, under certain assumptions, we give an explicit formula for the equivariant Euler characteristic $\chi ({\cal O}_X)={\rm H}^0(X, {\cal O}_X)-{\rm H}^1(X, {\cal O}_X)$ in the Grothendieck group of finitely generated ${\bf Z}[G]$-modules, when X is a curve over ${\bf Z}$ and G has prime order.

Type
Research Article
Copyright
© 2000 Kluwer Academic Publishers