{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J6PWEPW5ZIECK6VXPQSICCUFF6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c30e8e4a56f62aad00458d23bc16a929bf72f56ef08880c7e1009fd1e710d9b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-22T19:54:57Z","title_canon_sha256":"424b8268b3b0a6717488077f41f1780a411bfc3e935e037828eaacf0e66fcd17"},"schema_version":"1.0","source":{"id":"1305.5247","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5247","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5247v3","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5247","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"J6PWEPW5ZIEC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J6PWEPW5ZIECK6VX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J6PWEPW5","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:7ee961642f961cfe7e6dbabd749a34335034802f747efdae1f3822f859db961b","target":"graph","created_at":"2026-05-18T02:30:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Douglas Ulmer, Rachel Pries","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-22T19:54:57Z","title":"Arithmetic of abelian varieties in Artin-Schreier extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5247","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2e6c8ec12ab0e01c755b6e124197c61ecb0550b240803246ab36f30b0d606cf7","target":"record","created_at":"2026-05-18T02:30:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c30e8e4a56f62aad00458d23bc16a929bf72f56ef08880c7e1009fd1e710d9b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-22T19:54:57Z","title_canon_sha256":"424b8268b3b0a6717488077f41f1780a411bfc3e935e037828eaacf0e66fcd17"},"schema_version":"1.0","source":{"id":"1305.5247","kind":"arxiv","version":3}},"canonical_sha256":"4f9f623eddca08257ab77c24810a852f9b11c515f1568825acc8b0d258b06a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f9f623eddca08257ab77c24810a852f9b11c515f1568825acc8b0d258b06a43","first_computed_at":"2026-05-18T02:30:08.636298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:08.636298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s1avzIlgDmBn72XZ1aKmjYwmseqAFf7c5bVgglkGhbHfQpxNyqS5ZVF1ezX45fPT06PuWy61iXKb/yHthgjgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:08.636925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5247","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e6c8ec12ab0e01c755b6e124197c61ecb0550b240803246ab36f30b0d606cf7","sha256:7ee961642f961cfe7e6dbabd749a34335034802f747efdae1f3822f859db961b"],"state_sha256":"2ba1056b57e025fb5b709fc18409773ee5ecc3b4e8cbd3fa28437927be5884fe"}