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More precisely, for a smooth projective variety X, we show that the topological filtration T_pH_{2p+1}(X,Q) coincides with the geometric filtration G_pH_{2p+1}(X,Q) for all p. (Friedlander and Mazur had previously shown that T_pH_{2p}(X,Q})=G_pH_{2p}(X,Q)). As a corollary, we conclude t"},"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":"math/0603203","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-03-09T00:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"20ab4334b6e6caac3c7caec7d79016444617f476085abb0fa8640f2dedb28982","abstract_canon_sha256":"158c441d570aca4dbdabb52732e540fb8a563f3f90d6e4f12195a0a062c2a862"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:53:57.739667Z","signature_b64":"HvAxb+y94sTSOvUwS4ub5dBgfxkaYvcVcoZtmkWHK6xi79DzJftsj5jfvnBGHJL+RB6c/vS4XuedvASSAY6IDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43a1b5a9fabd20b9132d001b871465f554eea22d8968bed109d5d8554edd00a8","last_reissued_at":"2026-07-04T14:53:57.739329Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:53:57.739329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some relations between the topological and geometric filtration for smooth projective varieties","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2006-03-09T00:01:43Z","abstract_excerpt":"In the first part of this paper, we show that the assertion \"T_pH_k(X,Q)=G_pH_k(X,Q)\" (which is called the Friedlander-Mazur conjecture) is a birationally invariant statement for smooth projective varieties X when p=dim(X)-2 and when p=1. We also establish the Friedlander-Mazur conjecture in certain dimensions. More precisely, for a smooth projective variety X, we show that the topological filtration T_pH_{2p+1}(X,Q) coincides with the geometric filtration G_pH_{2p+1}(X,Q) for all p. (Friedlander and Mazur had previously shown that T_pH_{2p}(X,Q})=G_pH_{2p}(X,Q)). As a corollary, we conclude t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603203","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0603203/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0603203","created_at":"2026-07-04T14:53:57.739386+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0603203v1","created_at":"2026-07-04T14:53:57.739386+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603203","created_at":"2026-07-04T14:53:57.739386+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOQ3LKP2XUQL","created_at":"2026-07-04T14:53:57.739386+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOQ3LKP2XUQLSEZN","created_at":"2026-07-04T14:53:57.739386+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOQ3LKP2","created_at":"2026-07-04T14:53:57.739386+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V","json":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V.json","graph_json":"https://pith.science/api/pith-number/IOQ3LKP2XUQLSEZNAANYOFDF6V/graph.json","events_json":"https://pith.science/api/pith-number/IOQ3LKP2XUQLSEZNAANYOFDF6V/events.json","paper":"https://pith.science/paper/IOQ3LKP2"},"agent_actions":{"view_html":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V","download_json":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V.json","view_paper":"https://pith.science/paper/IOQ3LKP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0603203&json=true","fetch_graph":"https://pith.science/api/pith-number/IOQ3LKP2XUQLSEZNAANYOFDF6V/graph.json","fetch_events":"https://pith.science/api/pith-number/IOQ3LKP2XUQLSEZNAANYOFDF6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V/action/storage_attestation","attest_author":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V/action/author_attestation","sign_citation":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V/action/citation_signature","submit_replication":"https://pith.science/pith/IOQ3LKP2XUQLSEZNAANYOFDF6V/action/replication_record"}},"created_at":"2026-07-04T14:53:57.739386+00:00","updated_at":"2026-07-04T14:53:57.739386+00:00"}