{"paper":{"title":"Chow-Kuenneth decomposition for 3- and 4-folds fibred by varieties with small Chow group of zero-cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Charles Vial","submitted_at":"2011-11-15T21:28:11Z","abstract_excerpt":"Let $k$ be a field and let $\\Omega$ be a universal domain over $k$. Let $f:X \\r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $\\leq 2$ such that the general fibre of $f_\\Omega$ has trivial Chow group of zero-cycles. For example, $X$ could be the total space of a two-dimensional family of varieties whose general member is rationally connected. Suppose that $X$ has dimension $\\leq 4$. Then we prove that $X$ has a self-dual Murre decomposition, i.e. that $X$ has a self-dual Chow--Kuenneth decomposition which satisfi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3658","kind":"arxiv","version":2},"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"}