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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1104.4364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-21T22:54:42Z","cross_cats_sorted":[],"title_canon_sha256":"19cce5843555ea002da80ec93f61edcffa6fbb24051b09baeadf348023475ef2","abstract_canon_sha256":"954e5ed975423f9d6da62208f42847018e5bf5aa932325fec637191545b6f7bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:34.786722Z","signature_b64":"2RW6ZlU+x9Wqsmf2qcVk97FF07hD7BeJej724WmIkw1oCcvSaJ2aVdqPU0h4lIoaBHzqZ1lJRmtI0SODJ+CnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25494d51e8f704d853ef55927fa3374278795fcfea53cfb1915a3a9ff49c5302","last_reissued_at":"2026-05-18T04:23:34.786148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:34.786148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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