{"paper":{"title":"On the Weil-\\'etale topos of regular arithmetic schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Baptiste Morin, Matthias Flach","submitted_at":"2010-10-19T09:19:45Z","abstract_excerpt":"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 $\\zeta(X,s)$ 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 $\\zeta(X,s)$ and our cohomology groups recover those previously studied by Lichtenbaum and Geisser."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3833","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}