{"paper":{"title":"Cycles de codimension 2 et H^3 non ramifi\\'e pour les vari\\'et\\'es sur les corps finis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bruno Kahn, Jean-Louis Colliot-Th\\'el\\`ene","submitted_at":"2011-04-17T21:13:24Z","abstract_excerpt":"Let $X$ be a smooth projective variety over a finite field $\\F$. We discuss the unramified cohomology group $H^3_\\nr(X,\\Q/\\Z(2))$. Several conjectures put together imply that this group is finite. For certain classes of threefolds, $H^3_\\nr(X,\\Q/\\Z(2))$ actually vanishes. It is an open question whether this holds true for arbitrary threefolds. For a threefold $X$ equipped with a fibration onto a curve $C$, the generic fibre of which is a smooth projective surface $V$ over the global field $\\F(C)$, the vanishing of $H^3_\\nr(X,\\Q/\\Z(2))$ together with the Tate conjecture for divisors on $X$ impl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3350","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"}