Equivariant Euler–Poincaré characteristic in sheaf cohomology

Abstract

Let X be a topological Hausdorff space together with a continuous action of a finite group G. Let R be the ring of integers of a number field F . Let E be a G-sheaf of flat R-modules over X and let Φ be a G-stable paracompactifying family of supports on X. We show that under some natural cohomological finiteness conditions the Lefschetz number of the action of g ∈ G on the cohomology H •