The Weil-étale topology for number rings

Abstract

There should be a Grothendieck topology for an arithmetic scheme X such that the Euler characteristic of the cohomology groups of the constant sheaf Z with compact support at infinity gives, up to sign, the leading term of the zeta-function of X at s = 0. We construct a topology (the Weil-étale topology) for the ring of integers in a number field whose cohomology groups Hi (Z) determine such an Euler characterstic if we restrict to i ≤ 3.