Geodesic
On the Weil-étale topos of regular arithmetic schemes
Documenta mathematica, Tome 17 (2012), pp. 313-399.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We define and study a Weil-étale topos for any regular, proper scheme $\X$ over $\Spec(\bz)$ which has some of the properties suggested by Lichtenbaum for such a topos. In particular, the cohomology with $\tr$-coefficients has the expected relation to $\zeta(\X,s)$ at $s=0$ if the Hasse-Weil L-functions $L(h^i(\X_\bq),s)$ have the expected meromorphic continuation and functional equation. If $\X$ has characteristic $p$ the cohomology with $\bz$-coefficients also has the expected relation to $\zeta(\X,s)$ and our cohomology groups recover those previously studied by Lichtenbaum and Geisser.
Classification : 14F20, 11S40, 11G40, 18F10 
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     author = {Flach, Matthias and Morin, Baptiste},
     title = {On the {Weil-\'etale} topos of regular arithmetic schemes},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a19/}
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Flach, Matthias; Morin, Baptiste. On the Weil-étale topos of regular arithmetic schemes. Documenta mathematica, Tome 17 (2012), pp. 313-399. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a19/