Geodesic
The Weil-étale topology for number rings
Stephen Lichtenbaum1
1 Department of Mathematics<br/>Brown University<br/>Box 1917<br/>151 Thayer Street<br/>Providence, RI 02912<br/>United States
Annals of mathematics, Tome 170 (2009) no. 2, pp. 657-683.

Voir la notice de l'article provenant de la source Annals of Mathematics website

There should be a Grothendieck topology for an arithmetic scheme $X$ such that the Euler characteristic of the cohomology groups of the constant sheaf $\mathbb Z$ 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 $H^i(\mathbb Z) $ determine such an Euler characterstic if we restrict to $i\leq 3$.
DOI : 10.4007/annals.2009.170.657

Stephen Lichtenbaum 1

1 Department of Mathematics<br/>Brown University<br/>Box 1917<br/>151 Thayer Street<br/>Providence, RI 02912<br/>United States 
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Stephen Lichtenbaum. The Weil-étale topology for number rings. Annals of mathematics, Tome 170 (2009) no. 2, pp. 657-683. doi : 10.4007/annals.2009.170.657. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.657/

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