On the Weil-étale topos of regular arithmetic schemes
نویسنده
چکیده
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 R̃-coefficients has the expected relation to ζ(X , s) at s = 0 if the Hasse-Weil L-functions L(h(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. 2000 Mathematics Subject Classification: Primary: 14F20, 11S40, Secondary: 11G40, 18F10
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تاریخ انتشار 2010