{"paper":{"title":"Motivic obstruction to rationality of a very general cubic hypersurface in $\\mathbb P^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Vladimir Guletskii","submitted_at":"2016-05-30T22:16:22Z","abstract_excerpt":"Let $S$ be a smooth projective surface over a field. We introduce the notion of integral decomposability and, respectively, the opposite notion of integral indecomposability, of the transcendental motive $M^2_{\\rm tr}(S)$. If the transcendental motive is indecomposable rationally, then it is indecomposable integrally. For example, $M^2_{\\rm tr}(S)$ is rationally, and hence integrally indecomposable if $S$ is an algebraic $K3$-surface whose motive is known to be finite-dimensional. In the paper we prove that $M^2_{\\rm tr}(S)$ is integrally indecomposable when $S$ is the self-product of a smooth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09434","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"}