{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:J6PWEPW5ZIECK6VXPQSICCUFF6","short_pith_number":"pith:J6PWEPW5","schema_version":"1.0","canonical_sha256":"4f9f623eddca08257ab77c24810a852f9b11c515f1568825acc8b0d258b06a43","source":{"kind":"arxiv","id":"1305.5247","version":3},"attestation_state":"computed","paper":{"title":"Arithmetic of abelian varieties in Artin-Schreier extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Douglas Ulmer, Rachel Pries","submitted_at":"2013-05-22T19:54:57Z","abstract_excerpt":"We study abelian varieties defined over function fields of curves in positive characteristic $p$, focusing on their arithmetic within the system of Artin-Schreier extensions. First, we prove that the $L$-function of such an abelian variety vanishes to high order at the center point of its functional equation under a parity condition on the conductor. Second, we develop an Artin-Schreier variant of a construction of Berger. This yields a new class of Jacobians over function fields for which the Birch and Swinnerton-Dyer conjecture holds. Third, we give a formula for the rank of the Mordell-Weil"},"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":"1305.5247","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-22T19:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"424b8268b3b0a6717488077f41f1780a411bfc3e935e037828eaacf0e66fcd17","abstract_canon_sha256":"c30e8e4a56f62aad00458d23bc16a929bf72f56ef08880c7e1009fd1e710d9b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:08.636925Z","signature_b64":"s1avzIlgDmBn72XZ1aKmjYwmseqAFf7c5bVgglkGhbHfQpxNyqS5ZVF1ezX45fPT06PuWy61iXKb/yHthgjgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f9f623eddca08257ab77c24810a852f9b11c515f1568825acc8b0d258b06a43","last_reissued_at":"2026-05-18T02:30:08.636298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:08.636298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic of abelian varieties in Artin-Schreier extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Douglas Ulmer, Rachel Pries","submitted_at":"2013-05-22T19:54:57Z","abstract_excerpt":"We study abelian varieties defined over function fields of curves in positive characteristic $p$, focusing on their arithmetic within the system of Artin-Schreier extensions. First, we prove that the $L$-function of such an abelian variety vanishes to high order at the center point of its functional equation under a parity condition on the conductor. Second, we develop an Artin-Schreier variant of a construction of Berger. This yields a new class of Jacobians over function fields for which the Birch and Swinnerton-Dyer conjecture holds. Third, we give a formula for the rank of the Mordell-Weil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5247","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":""},"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":"1305.5247","created_at":"2026-05-18T02:30:08.636429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5247v3","created_at":"2026-05-18T02:30:08.636429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5247","created_at":"2026-05-18T02:30:08.636429+00:00"},{"alias_kind":"pith_short_12","alias_value":"J6PWEPW5ZIEC","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"J6PWEPW5ZIECK6VX","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"J6PWEPW5","created_at":"2026-05-18T12:27:49.015174+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/J6PWEPW5ZIECK6VXPQSICCUFF6","json":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6.json","graph_json":"https://pith.science/api/pith-number/J6PWEPW5ZIECK6VXPQSICCUFF6/graph.json","events_json":"https://pith.science/api/pith-number/J6PWEPW5ZIECK6VXPQSICCUFF6/events.json","paper":"https://pith.science/paper/J6PWEPW5"},"agent_actions":{"view_html":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6","download_json":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6.json","view_paper":"https://pith.science/paper/J6PWEPW5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5247&json=true","fetch_graph":"https://pith.science/api/pith-number/J6PWEPW5ZIECK6VXPQSICCUFF6/graph.json","fetch_events":"https://pith.science/api/pith-number/J6PWEPW5ZIECK6VXPQSICCUFF6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6/action/storage_attestation","attest_author":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6/action/author_attestation","sign_citation":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6/action/citation_signature","submit_replication":"https://pith.science/pith/J6PWEPW5ZIECK6VXPQSICCUFF6/action/replication_record"}},"created_at":"2026-05-18T02:30:08.636429+00:00","updated_at":"2026-05-18T02:30:08.636429+00:00"}