The Weil-Etale Topology for Number Rings

2005/03/25 by Stephen Lichtenbaum, Lichtenbaum, Stephen · 1 citation
Mathematics · #11R42 #14F20 #14F42 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11R42 #msc:14F20 #msc:14F42

paper · pdf · doi:10.48550/arxiv.math/0503604

31 pages

arxiv created 2005/03/25 · arxiv updated 2009/12/01

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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