• Corpus ID: 2342668

On the Weil-Étale Topos of Regular Arithmetic Schemes

  title={On the Weil-{\'E}tale Topos of Regular Arithmetic Schemes},
  author={Matthias Flach and Baptiste Morin},
  journal={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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