Geodesic
On the Weil-étale topos of regular arithmetic schemes
Documenta mathematica, Tome 17 (2012), pp. 313-399
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We define and study a Weil-étale topos for any regular, proper scheme X over Spec(Z) which has some of the properties suggested by Lichtenbaum for such a topos. In particular, the cohomology with R~-coefficients has the expected relation to ζ(X,s) at s=0 if the Hasse–Weil L-functions L(hi(XQ​),s) have the expected meromorphic continuation and functional equation. If X has characteristic p the cohomology with Z-coefficients also has the expected relation to ζ(X,s) and our cohomology groups recover those previously studied by Lichtenbaum and Geisser.
DOI : 10.4171/dm/369
Classification : 11G40, 11S40, 14F20, 18F10 
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     author = {Matthias Flach and Baptiste Morin},
     title = {On the {Weil-\'etale} topos of regular arithmetic schemes},
     journal = {Documenta mathematica},
     pages = {313--399},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/369},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/369/}
}
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Matthias Flach; Baptiste Morin. On the Weil-étale topos of regular arithmetic schemes. Documenta mathematica, Tome 17 (2012), pp. 313-399. doi: 10.4171/dm/369

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