Abstract
Let X be a Hausdorff space equipped with a continuous action of a finite group G and a G-stable family of supports \({\Phi}\). Fix a number field F with ring of integers R. We study the class \({\chi = \sum_j (-1)^j [H^j_\Phi (X, \mathcal{E}) \otimes_R F]}\) in the character group of G over F for any flat G-sheaf \({\mathcal{E}}\) of R-modules over X. Under natural cohomological finiteness conditions we give a formula for \({\chi}\) with respect to the basis given by the irreducible characters of G. We discuss applications of our result concerning the cohomology of arithmetic groups.
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Steffen Kionke acknowledges the generous support of the Max-Planck Institute in Bonn.
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Kionke, S., Rohlfs, J. Equivariant Euler–Poincaré characteristic in sheaf cohomology. manuscripta math. 149, 283–295 (2016). https://doi.org/10.1007/s00229-015-0784-0
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DOI: https://doi.org/10.1007/s00229-015-0784-0