{"paper":{"title":"Quelques cas d'annulation du troisi\\`eme groupe de cohomologie non ramifi\\'ee","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Jean-Louis Colliot-Th\\'el\\`ene","submitted_at":"2011-10-06T20:33:29Z","abstract_excerpt":"The third unramified cohomology group is shown to vanish on certain varieties equipped with a pencil of quadrics or of smooth complete intersections of two quadrics. Over the complex field, this shows that the integral Hodge conjecture in degree 4 holds for such varieties.\n  ---\n  On \\'etablit la nullit\\'e du troisi\\`eme groupe de cohomologie non ramifi\\'ee pour certaines vari\\'et\\'es munies d'un pinceau de quadriques ou d'intersections compl\\`etes lisses de deux quadriques. Sur les complexes, ceci permet d'\\'etablir la conjecture de Hodge enti\\`ere en degr\\'e 4 pour de telles vari\\'et\\'es."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1389","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"}