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The Weil-étale topology on schemes over finite fields

Published online by Cambridge University Press:  21 April 2005

S. Lichtenbaum
S. Lichtenbaum
Affiliation:
Mathematics Department, Brown University, 151 Thayer Street, Providence, RI 02912, [email protected]
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Abstract

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We introduce an essentially new Grothendieck topology, the Weil-étale topology, on schemes over finite fields. The cohomology groups associated with this topology should behave better than the standard étale cohomology groups. In particular there is a very natural definition of an Euler characteristic and a plausible conjecture relating the Euler characteristic of Z to the value of the zeta-function at s = 0. This conjecture is proved in certain cases.

Keywords

étale cohomologyzeta-functions14F20 (primary)14G10 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 3 , May 2005 , pp. 689 - 702
Copyright
Foundation Compositio Mathematica 2005