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Published 2012 | public
Journal Article

On the Weil-Étale Topos of Regular Arithmetic Schemes

Abstract

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(h^(i)(X_(Q)), 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.

Additional Information

The first author is supported by grant DMS-0701029 from the National Science Foundation. He would also like to thank Spencer Bloch for a helpful discussion about the material in section 10 and the MPI Bonn for its hospitality during the final preparation of this paper.

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023