{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:73MHDMCAW5MLNMMJ32SC5HV6KT","short_pith_number":"pith:73MHDMCA","schema_version":"1.0","canonical_sha256":"fed871b040b758b6b189dea42e9ebe54fc1d3deaa4a34820166e9e104626ed6b","source":{"kind":"arxiv","id":"1405.2777","version":2},"attestation_state":"computed","paper":{"title":"Iwasawa theory of Heegner cycles, I. Rank over the Iwasawa algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Matteo Longo, Stefano Vigni","submitted_at":"2014-05-12T14:26:49Z","abstract_excerpt":"Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper, the first in a series of two, is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne's p-adic representation attached to a modular form f of even weight >2. In this more general setting, the role of Heegner points is played by higher-dimensional Heegner cycles in the sense of Nekov\\'a\\v{r}. In particular, we prove that the Pontryagin dual of a certain Blo"},"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":"1405.2777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-12T14:26:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8f96667c7255b088b9be6ff031379e7c16653acc30dffabe648eb243abb916cc","abstract_canon_sha256":"5fecbb992a9bd133e73917841b3e10e2c6aef1dc6dc5629ddf34c064f5b3e181"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:41.272203Z","signature_b64":"0h+4PetbONCGoe8xgSvbcDJDJXR/3qMvPMO94CDDAXR5p10IRUxiR61mR9MdnDLim9U7rNTLDga1FPJPas+MCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fed871b040b758b6b189dea42e9ebe54fc1d3deaa4a34820166e9e104626ed6b","last_reissued_at":"2026-05-18T02:51:41.271783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:41.271783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iwasawa theory of Heegner cycles, I. Rank over the Iwasawa algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Matteo Longo, Stefano Vigni","submitted_at":"2014-05-12T14:26:49Z","abstract_excerpt":"Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper, the first in a series of two, is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne's p-adic representation attached to a modular form f of even weight >2. In this more general setting, the role of Heegner points is played by higher-dimensional Heegner cycles in the sense of Nekov\\'a\\v{r}. In particular, we prove that the Pontryagin dual of a certain Blo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2777","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1405.2777","created_at":"2026-05-18T02:51:41.271839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.2777v2","created_at":"2026-05-18T02:51:41.271839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2777","created_at":"2026-05-18T02:51:41.271839+00:00"},{"alias_kind":"pith_short_12","alias_value":"73MHDMCAW5ML","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"73MHDMCAW5MLNMMJ","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"73MHDMCA","created_at":"2026-05-18T12:28:16.859392+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/73MHDMCAW5MLNMMJ32SC5HV6KT","json":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT.json","graph_json":"https://pith.science/api/pith-number/73MHDMCAW5MLNMMJ32SC5HV6KT/graph.json","events_json":"https://pith.science/api/pith-number/73MHDMCAW5MLNMMJ32SC5HV6KT/events.json","paper":"https://pith.science/paper/73MHDMCA"},"agent_actions":{"view_html":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT","download_json":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT.json","view_paper":"https://pith.science/paper/73MHDMCA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.2777&json=true","fetch_graph":"https://pith.science/api/pith-number/73MHDMCAW5MLNMMJ32SC5HV6KT/graph.json","fetch_events":"https://pith.science/api/pith-number/73MHDMCAW5MLNMMJ32SC5HV6KT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT/action/storage_attestation","attest_author":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT/action/author_attestation","sign_citation":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT/action/citation_signature","submit_replication":"https://pith.science/pith/73MHDMCAW5MLNMMJ32SC5HV6KT/action/replication_record"}},"created_at":"2026-05-18T02:51:41.271839+00:00","updated_at":"2026-05-18T02:51:41.271839+00:00"}