{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HBYOGMKLZ5TI5NQE5X6MG2WSJJ","short_pith_number":"pith:HBYOGMKL","schema_version":"1.0","canonical_sha256":"3870e3314bcf668eb604edfcc36ad24a6688d801b6e3e11a5d27defecb6ef14d","source":{"kind":"arxiv","id":"1306.1708","version":2},"attestation_state":"computed","paper":{"title":"$(\\varphi,\\Gamma)$-modules associ\\'es aux courbes hyperelliptiques lisses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christine Huyghe, Nathalie Wach","submitted_at":"2013-06-07T12:46:15Z","abstract_excerpt":"In 2003, Kedlaya gave an algorithm to compute the zeta function associated to a hyperelliptic curve over a finite field, by computing the rigid cohomology of the curve. Edixhoven remarked that it is actually possible to compute the crystalline cohomology of the curve, which is a lattice in the rigid cohomology. Following a method of Wach, we first explain how to use this lattice to compute the $(\\varphi,\\Gamma)$-module associated to an hyperelliptic curve. We also explain an alternative way to get the $(\\varphi,\\Gamma)$-module mod $p$ that relies on the Deligne-Illusie morphism."},"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":"1306.1708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-07T12:46:15Z","cross_cats_sorted":[],"title_canon_sha256":"fa35bcf282e98218e6e024fb10df7f4b756fe4c8647dbfdb55140c753059237b","abstract_canon_sha256":"c77235b70e28d2a407bb485ceab6f59224b4811173d8d9af045294be56f203d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:32.083252Z","signature_b64":"u6ZRdFQ4AbWN7hoy1t+aXDxKVpgHNFxYD2APH5QhXfHB1aHE+rGBFGCvBwbdl2BlrmtKQK2ACesRvmnvZ/+LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3870e3314bcf668eb604edfcc36ad24a6688d801b6e3e11a5d27defecb6ef14d","last_reissued_at":"2026-05-18T03:03:32.082779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:32.082779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$(\\varphi,\\Gamma)$-modules associ\\'es aux courbes hyperelliptiques lisses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christine Huyghe, Nathalie Wach","submitted_at":"2013-06-07T12:46:15Z","abstract_excerpt":"In 2003, Kedlaya gave an algorithm to compute the zeta function associated to a hyperelliptic curve over a finite field, by computing the rigid cohomology of the curve. Edixhoven remarked that it is actually possible to compute the crystalline cohomology of the curve, which is a lattice in the rigid cohomology. Following a method of Wach, we first explain how to use this lattice to compute the $(\\varphi,\\Gamma)$-module associated to an hyperelliptic curve. We also explain an alternative way to get the $(\\varphi,\\Gamma)$-module mod $p$ that relies on the Deligne-Illusie morphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1708","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":"1306.1708","created_at":"2026-05-18T03:03:32.082850+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1708v2","created_at":"2026-05-18T03:03:32.082850+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1708","created_at":"2026-05-18T03:03:32.082850+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBYOGMKLZ5TI","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBYOGMKLZ5TI5NQE","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBYOGMKL","created_at":"2026-05-18T12:27:46.883200+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/HBYOGMKLZ5TI5NQE5X6MG2WSJJ","json":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ.json","graph_json":"https://pith.science/api/pith-number/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/graph.json","events_json":"https://pith.science/api/pith-number/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/events.json","paper":"https://pith.science/paper/HBYOGMKL"},"agent_actions":{"view_html":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ","download_json":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ.json","view_paper":"https://pith.science/paper/HBYOGMKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1708&json=true","fetch_graph":"https://pith.science/api/pith-number/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/graph.json","fetch_events":"https://pith.science/api/pith-number/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/action/storage_attestation","attest_author":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/action/author_attestation","sign_citation":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/action/citation_signature","submit_replication":"https://pith.science/pith/HBYOGMKLZ5TI5NQE5X6MG2WSJJ/action/replication_record"}},"created_at":"2026-05-18T03:03:32.082850+00:00","updated_at":"2026-05-18T03:03:32.082850+00:00"}