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15 May 2006 Arithmetic cohomology over finite fields and special values of ζ-functions
Thomas Geisser
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Duke Math. J. 133(1): 27-57 (15 May 2006). DOI: 10.1215/S0012-7094-06-13312-4

Abstract

We construct cohomology groups with compact support Hci(Xar,Z(n)) for separated schemes of finite type over a finite field which generalize Lichtenbaum's Weil-étale cohomology groups for smooth and projective schemes (see [22]). In particular, if Tate's conjecture holds, and rational and numerical equivalence agree up to torsion, then the groups Hci(Xar,Z(n)) are finitely generated, form an integral model of l-adic cohomology with compact support, and admit a formula for the special values of the ζ-function of X

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Thomas Geisser. "Arithmetic cohomology over finite fields and special values of ζ-functions." Duke Math. J. 133 (1) 27 - 57, 15 May 2006. https://doi.org/10.1215/S0012-7094-06-13312-4

Information

Published: 15 May 2006
First available in Project Euclid: 19 April 2006

zbMATH: 1104.14011
MathSciNet: MR2219269
Digital Object Identifier: 10.1215/S0012-7094-06-13312-4

Subjects:
Primary: 14F20
Secondary: 11G25, 14F42

Rights: Copyright © 2006 Duke University Press

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Vol.133 • No. 1 • 15 May 2006
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