{"paper":{"title":"Beilinson's Hodge conjecture for smooth varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"James D. Lewis, Rob de Jeu","submitted_at":"2011-04-21T22:54:42Z","abstract_excerpt":"Consider the cycle class map cl_{r,m} : CH^r(U,m;\\Q) \\to \\Gamma H^{2r-m}(U,\\Q(r)), where CH^r(U,m;\\Q) is Bloch's higher Chow group (tensored with \\Q) of a smooth complex quasi-projective variety U, and H^{2r-m}(U,\\Q(r)) is singular cohomology. We study the image of cl_{r,m} in terms of kernels of Abel-Jacobi maps. When r=m, we deduce from the Bloch-Kato theorem that the cokernel of cl_{r,m} at the generic point of U is the same for integral or rational coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4364","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"}