Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T21:09:06.762Z Has data issue: false hasContentIssue false

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: pappas@math.msu.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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