{"paper":{"title":"Weil-\\'etale cohomology and Zeta-values of proper 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":"2016-05-04T13:44:48Z","abstract_excerpt":"We give a conjectural description of the vanishing order and leading Taylor coefficient of the Zeta function of a proper, regular arithmetic scheme $\\mathcal{X}$ at any integer $n$ in terms of Weil-\\'etale cohomology complexes. This extends work of Lichtenbaum \\cite{Lichtenbaum05} and Geisser \\cite{Geisser04b} for $\\mathcal{X}$ of characteristic $p$, of Lichtenbaum \\cite{li04} for $\\mathcal{X}=\\mathrm{Spec}(\\mathcal{O}_F)$ and $n=0$ where $F$ is a number field, and of the second author for arbitrary $\\mathcal{X}$ and $n=0$ \\cite{Morin14}. We show that our conjecture is compatible with the Tama"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01277","kind":"arxiv","version":2},"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"}