# The Weil-étale topology for number rings | Annals of Mathematics

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.

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### 数学年刊（Annals of Mathematics）

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