{"paper":{"title":"Index of varieties over Henselian fields and Euler characteristic of coherent sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"H\\'el\\`ene Esnault, Marc Levine, Olivier Wittenberg","submitted_at":"2012-07-08T15:49:21Z","abstract_excerpt":"Let X be a smooth proper variety over the quotient field of a Henselian discrete valuation ring with algebraically closed residue field of characteristic p. We show that for any coherent sheaf E on X, the index of X divides the Euler-Poincar\\'e characteristic \\chi(X,E) if p=0 or p>dim(X)+1. If 0<p\\leq dim(X)+1, the prime-to-p part of the index of X divides \\chi(X,E). Combining this with the Hattori-Stong theorem yields an analogous result concerning the divisibility of the cobordism class of X by the index of X.\n  As a corollary, rationally connected varieties over the maximal unramified exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1883","kind":"arxiv","version":3},"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"}