{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:DDVW522446GW5SHVQW2NTUYMDW","short_pith_number":"pith:DDVW5224","schema_version":"1.0","canonical_sha256":"18eb6eeb5ce78d6ec8f585b4d9d30c1da05e8af2aeacae6e3f688aa87aa541c7","source":{"kind":"arxiv","id":"math/0310162","version":1},"attestation_state":"computed","paper":{"title":"Algebraic cycles on Hilbert modular fourfolds and poles of L-functions","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan","submitted_at":"2003-10-11T00:40:57Z","abstract_excerpt":"In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence subgroups \\Gamma of SL(2, O_K), where O_K denotes the ring of integers of a quartic, Galois, totally real number field K. The expected relationship to the orders of poles of the associated L-functions is verified for abelian extensions of \\Q. Also shown is the existence of homologically non-trivial cycles of codimension two which are not intersections of divis"},"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/0310162","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2003-10-11T00:40:57Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"776887d5817cebf47ebc86f2ecace007807750d82541bcbf93026cb70aa071ad","abstract_canon_sha256":"05afc6a6dbc7b114006756251b8d7eb98770d60a4064012d322d4b96e6375c69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:47.071744Z","signature_b64":"xLj5midfUXA/qTFXYxfOzdgm6lqPcdU9nQEJLDRNOly0MsfSNyLqSvEwgPrOOhvc6Q16+Z0X8lH4BNHH3itxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18eb6eeb5ce78d6ec8f585b4d9d30c1da05e8af2aeacae6e3f688aa87aa541c7","last_reissued_at":"2026-07-04T14:37:47.071337Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:47.071337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic cycles on Hilbert modular fourfolds and poles of L-functions","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan","submitted_at":"2003-10-11T00:40:57Z","abstract_excerpt":"In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence subgroups \\Gamma of SL(2, O_K), where O_K denotes the ring of integers of a quartic, Galois, totally real number field K. The expected relationship to the orders of poles of the associated L-functions is verified for abelian extensions of \\Q. Also shown is the existence of homologically non-trivial cycles of codimension two which are not intersections of divis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310162","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/0310162/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/0310162","created_at":"2026-07-04T14:37:47.071398+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0310162v1","created_at":"2026-07-04T14:37:47.071398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310162","created_at":"2026-07-04T14:37:47.071398+00:00"},{"alias_kind":"pith_short_12","alias_value":"DDVW522446GW","created_at":"2026-07-04T14:37:47.071398+00:00"},{"alias_kind":"pith_short_16","alias_value":"DDVW522446GW5SHV","created_at":"2026-07-04T14:37:47.071398+00:00"},{"alias_kind":"pith_short_8","alias_value":"DDVW5224","created_at":"2026-07-04T14:37:47.071398+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/DDVW522446GW5SHVQW2NTUYMDW","json":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW.json","graph_json":"https://pith.science/api/pith-number/DDVW522446GW5SHVQW2NTUYMDW/graph.json","events_json":"https://pith.science/api/pith-number/DDVW522446GW5SHVQW2NTUYMDW/events.json","paper":"https://pith.science/paper/DDVW5224"},"agent_actions":{"view_html":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW","download_json":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW.json","view_paper":"https://pith.science/paper/DDVW5224","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0310162&json=true","fetch_graph":"https://pith.science/api/pith-number/DDVW522446GW5SHVQW2NTUYMDW/graph.json","fetch_events":"https://pith.science/api/pith-number/DDVW522446GW5SHVQW2NTUYMDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW/action/storage_attestation","attest_author":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW/action/author_attestation","sign_citation":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW/action/citation_signature","submit_replication":"https://pith.science/pith/DDVW522446GW5SHVQW2NTUYMDW/action/replication_record"}},"created_at":"2026-07-04T14:37:47.071398+00:00","updated_at":"2026-07-04T14:37:47.071398+00:00"}