• Corpus ID: 2342668

# On the Weil-Étale Topos of Regular Arithmetic Schemes

@article{Flach2012OnTW,
title={On the Weil-{\'E}tale Topos of Regular Arithmetic Schemes},
author={Matthias Flach and Baptiste Morin},
journal={arXiv: Number Theory},
year={2012}
}
• Published 19 October 2010
• Mathematics
• arXiv: Number Theory
We define and study a Weil-etale 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…

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