Nearly perfect complexes and Galois module structure

Chinberg, T., Kolster, M., Pappus, G. and Snaith, V. (1999) Nearly perfect complexes and Galois module structure. Compositio Mathematica, 119 (2), 133-155. (doi:10.1023/A:1001716302575).

Abstract

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.

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