{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:LELWOTSOCKE2PHQ3OQ6P25MCJL","short_pith_number":"pith:LELWOTSO","schema_version":"1.0","canonical_sha256":"5917674e4e1289a79e1b743cfd75824ad02b1c07c6bc3e17e90e3159501b6514","source":{"kind":"arxiv","id":"2110.13102","version":3},"attestation_state":"computed","paper":{"title":"On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Loeffler, Sarah Livia Zerbes","submitted_at":"2021-10-25T16:54:39Z","abstract_excerpt":"Let $A$ be a modular abelian surface over $Q$ which either has trivial geometric endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an imaginary quadratic field which is modular and is not a $Q$-curve. In the former case, assume that there exists an odd Dirichlet character $\\chi$ such that $L(A,\\chi,1)\\neq 0$. We prove the following implication: if $L(A, 1) \\ne 0$, and the $p$-adic eigenvariety for $GSp_4$ is smooth at the point corresponding to $A$ (and some auxiliary technical hypotheses hold), then $A(Q)$ is finite, as predicted by the Birch--Swinnerton-Dye"},"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":"2110.13102","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-10-25T16:54:39Z","cross_cats_sorted":[],"title_canon_sha256":"1833eb5b5f8b61b3f51f44c7afe87e1016e8e83a028f6e5ecc61d98f64bf06a9","abstract_canon_sha256":"2ade93682e98e44867ae3cb37e016b15516c163aa93ed03617856beafe5b7c0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:30:23.798712Z","signature_b64":"Z2VqCKSE0jyYgbcyvqnNQVUv/92Pm+mM0begVOV9hi9wKqUFndDTB8onxBKUEGypt+XfOrRAgrEdhQBC9aS+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5917674e4e1289a79e1b743cfd75824ad02b1c07c6bc3e17e90e3159501b6514","last_reissued_at":"2026-07-05T06:30:23.798237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:30:23.798237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Loeffler, Sarah Livia Zerbes","submitted_at":"2021-10-25T16:54:39Z","abstract_excerpt":"Let $A$ be a modular abelian surface over $Q$ which either has trivial geometric endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an imaginary quadratic field which is modular and is not a $Q$-curve. In the former case, assume that there exists an odd Dirichlet character $\\chi$ such that $L(A,\\chi,1)\\neq 0$. We prove the following implication: if $L(A, 1) \\ne 0$, and the $p$-adic eigenvariety for $GSp_4$ is smooth at the point corresponding to $A$ (and some auxiliary technical hypotheses hold), then $A(Q)$ is finite, as predicted by the Birch--Swinnerton-Dye"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.13102","kind":"arxiv","version":3},"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/2110.13102/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":"2110.13102","created_at":"2026-07-05T06:30:23.798294+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.13102v3","created_at":"2026-07-05T06:30:23.798294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.13102","created_at":"2026-07-05T06:30:23.798294+00:00"},{"alias_kind":"pith_short_12","alias_value":"LELWOTSOCKE2","created_at":"2026-07-05T06:30:23.798294+00:00"},{"alias_kind":"pith_short_16","alias_value":"LELWOTSOCKE2PHQ3","created_at":"2026-07-05T06:30:23.798294+00:00"},{"alias_kind":"pith_short_8","alias_value":"LELWOTSO","created_at":"2026-07-05T06:30:23.798294+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.00876","citing_title":"The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL","json":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL.json","graph_json":"https://pith.science/api/pith-number/LELWOTSOCKE2PHQ3OQ6P25MCJL/graph.json","events_json":"https://pith.science/api/pith-number/LELWOTSOCKE2PHQ3OQ6P25MCJL/events.json","paper":"https://pith.science/paper/LELWOTSO"},"agent_actions":{"view_html":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL","download_json":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL.json","view_paper":"https://pith.science/paper/LELWOTSO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.13102&json=true","fetch_graph":"https://pith.science/api/pith-number/LELWOTSOCKE2PHQ3OQ6P25MCJL/graph.json","fetch_events":"https://pith.science/api/pith-number/LELWOTSOCKE2PHQ3OQ6P25MCJL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL/action/storage_attestation","attest_author":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL/action/author_attestation","sign_citation":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL/action/citation_signature","submit_replication":"https://pith.science/pith/LELWOTSOCKE2PHQ3OQ6P25MCJL/action/replication_record"}},"created_at":"2026-07-05T06:30:23.798294+00:00","updated_at":"2026-07-05T06:30:23.798294+00:00"}