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The Weil-Etale Topology for Number Rings

Stephen Lichtenbaum
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Abstract

We would like to construct a new Grothendieck topology for arithmetic schemes, whose cohomology groups associated with motivic complexes of sheaves are finitely generated and whose Euler characteristics are related to special values of zeta-functions. In this paper we construct this topology for rings of algebraic integers and show that the cohomology of the constant sheaf Z is related to the behavior of zeta-functions at s = 0.

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Stephen Lichtenbaum. 2005-03-25. The Weil-Etale Topology for Number Rings. https://arxiv.org/abs/math/0503604

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