{"paper":{"title":"Hypersurfaces quartiques de dimension 3 : non rationalit\\'e stable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alena Pirutka, Jean-Louis Colliot-Th\\'el\\`ene","submitted_at":"2014-02-17T21:34:00Z","abstract_excerpt":"Inspir\\'es par un argument de C. Voisin, nous montrons l'existence d'hypersurfaces quartiques lisses dans ${\\bf P}^4_{\\mathbb C}$ qui ne sont pas stablement rationnelles, plus pr\\'ecis\\'ement dont le groupe de Chow de degr\\'e z\\'ero n'est pas universellement \\'egal \\`a $\\mathbb Z$.\n  ---\n  There are (many) smooth quartic hypersurfaces in ${\\bf P}^4_{\\mathbb C}$ which are not stably rational. More precisely, their degree zero Chow group is not universally equal to $\\mathbb Z$. The proof uses a variation of a specialisation method due to C. Voisin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4153","kind":"arxiv","version":4},"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"}