{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NMMHTBPSQ2IVAV2S6TIFKQJYAZ","short_pith_number":"pith:NMMHTBPS","schema_version":"1.0","canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","source":{"kind":"arxiv","id":"1708.03652","version":1},"attestation_state":"computed","paper":{"title":"Non-ordinary curves with a Prym variety of low $p$-rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Burcin Gunes, Ekin Ozman, Lara Thomas, Rachel Newton, Rachel Pries, Turku Ozlum Celik, Yara Elias","submitted_at":"2017-08-11T18:25:30Z","abstract_excerpt":"If $\\pi: Y \\to X$ is an unramified double cover of a smooth curve of genus $g$, then the Prym variety $P_\\pi$ is a principally polarized abelian variety of dimension $g-1$. When $X$ is defined over an algebraically closed field $k$ of characteristic $p$, it is not known in general which $p$-ranks can occur for $P_\\pi$ under restrictions on the $p$-rank of $X$. In this paper, when $X$ is a non-hyperelliptic curve of genus $g=3$, we analyze the relationship between the Hasse-Witt matrices of $X$ and $P_\\pi$. As an application, when $p \\equiv 5 \\bmod 6$, we prove that there exists a curve $X$ of "},"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":"1708.03652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-11T18:25:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1ee87b84af8487932485c0c04f243a17d07aaa3d226e6013c705bbcec282e6fa","abstract_canon_sha256":"746856bc22f5590b452c13b7ffc0b4214a52c00d6348e4ff8e289e914f807206"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:08.236818Z","signature_b64":"IxAwXdYvuXa8WMQ9Mg24dhrrQhD/q8cuJ3OFhDMxQGQDAnue6buYRMhW54ATJGi7aSe21zssBQQ33zLxm40HBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","last_reissued_at":"2026-05-18T00:38:08.236305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:08.236305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-ordinary curves with a Prym variety of low $p$-rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Burcin Gunes, Ekin Ozman, Lara Thomas, Rachel Newton, Rachel Pries, Turku Ozlum Celik, Yara Elias","submitted_at":"2017-08-11T18:25:30Z","abstract_excerpt":"If $\\pi: Y \\to X$ is an unramified double cover of a smooth curve of genus $g$, then the Prym variety $P_\\pi$ is a principally polarized abelian variety of dimension $g-1$. When $X$ is defined over an algebraically closed field $k$ of characteristic $p$, it is not known in general which $p$-ranks can occur for $P_\\pi$ under restrictions on the $p$-rank of $X$. In this paper, when $X$ is a non-hyperelliptic curve of genus $g=3$, we analyze the relationship between the Hasse-Witt matrices of $X$ and $P_\\pi$. As an application, when $p \\equiv 5 \\bmod 6$, we prove that there exists a curve $X$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03652","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":""},"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":"1708.03652","created_at":"2026-05-18T00:38:08.236389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03652v1","created_at":"2026-05-18T00:38:08.236389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03652","created_at":"2026-05-18T00:38:08.236389+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMMHTBPSQ2IV","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMMHTBPSQ2IVAV2S","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMMHTBPS","created_at":"2026-05-18T12:31:34.259226+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/NMMHTBPSQ2IVAV2S6TIFKQJYAZ","json":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ.json","graph_json":"https://pith.science/api/pith-number/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/graph.json","events_json":"https://pith.science/api/pith-number/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/events.json","paper":"https://pith.science/paper/NMMHTBPS"},"agent_actions":{"view_html":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ","download_json":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ.json","view_paper":"https://pith.science/paper/NMMHTBPS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03652&json=true","fetch_graph":"https://pith.science/api/pith-number/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/action/storage_attestation","attest_author":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/action/author_attestation","sign_citation":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/action/citation_signature","submit_replication":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/action/replication_record"}},"created_at":"2026-05-18T00:38:08.236389+00:00","updated_at":"2026-05-18T00:38:08.236389+00:00"}