{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4P3FN2G35BRXNKJFMGRKHO5T3X","short_pith_number":"pith:4P3FN2G3","schema_version":"1.0","canonical_sha256":"e3f656e8dbe86376a92561a2a3bbb3ddfd650703ab1eb2a32f54a97a1ef3d4af","source":{"kind":"arxiv","id":"1907.05838","version":1},"attestation_state":"computed","paper":{"title":"Tamagawa number formula with coefficients over varieties in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Fabien Trihan, Olivier Brinon","submitted_at":"2019-07-12T16:58:54Z","abstract_excerpt":"We express the order of the pole and the leading coefficient of the L-function of a (large class of) -adic coefficients (any prime) over a quasi-projective variety over a finite field of characteristic p. This is a generalization of the result of Milne-Ramachandran with coefficients. The new key ingredient is the use of F-gauges and their equivalence in the derived category with Raynaud modules proved by Ekedahl."},"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":"1907.05838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-12T16:58:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"91df640ec223274db9100798d76d9297a6a301f26b4aa62b6371e8ce1e93956f","abstract_canon_sha256":"7538aea01d1f2c0c2e77b8c6661422e28a05854fce5dce05a968ccf1de4a9d23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:44.243024Z","signature_b64":"iwN6QvomSu1NKcRlODjmrQDvAEv0g1/gg/0+HPSrSyg0eKXo0rkXd/y/Wp3p/PMXT+RPCsJDK7670peO0NVkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3f656e8dbe86376a92561a2a3bbb3ddfd650703ab1eb2a32f54a97a1ef3d4af","last_reissued_at":"2026-05-17T23:40:44.242546Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:44.242546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tamagawa number formula with coefficients over varieties in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Fabien Trihan, Olivier Brinon","submitted_at":"2019-07-12T16:58:54Z","abstract_excerpt":"We express the order of the pole and the leading coefficient of the L-function of a (large class of) -adic coefficients (any prime) over a quasi-projective variety over a finite field of characteristic p. This is a generalization of the result of Milne-Ramachandran with coefficients. The new key ingredient is the use of F-gauges and their equivalence in the derived category with Raynaud modules proved by Ekedahl."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05838","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":"1907.05838","created_at":"2026-05-17T23:40:44.242617+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05838v1","created_at":"2026-05-17T23:40:44.242617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05838","created_at":"2026-05-17T23:40:44.242617+00:00"},{"alias_kind":"pith_short_12","alias_value":"4P3FN2G35BRX","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4P3FN2G35BRXNKJF","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4P3FN2G3","created_at":"2026-05-18T12:33:10.108867+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/4P3FN2G35BRXNKJFMGRKHO5T3X","json":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X.json","graph_json":"https://pith.science/api/pith-number/4P3FN2G35BRXNKJFMGRKHO5T3X/graph.json","events_json":"https://pith.science/api/pith-number/4P3FN2G35BRXNKJFMGRKHO5T3X/events.json","paper":"https://pith.science/paper/4P3FN2G3"},"agent_actions":{"view_html":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X","download_json":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X.json","view_paper":"https://pith.science/paper/4P3FN2G3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05838&json=true","fetch_graph":"https://pith.science/api/pith-number/4P3FN2G35BRXNKJFMGRKHO5T3X/graph.json","fetch_events":"https://pith.science/api/pith-number/4P3FN2G35BRXNKJFMGRKHO5T3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X/action/storage_attestation","attest_author":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X/action/author_attestation","sign_citation":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X/action/citation_signature","submit_replication":"https://pith.science/pith/4P3FN2G35BRXNKJFMGRKHO5T3X/action/replication_record"}},"created_at":"2026-05-17T23:40:44.242617+00:00","updated_at":"2026-05-17T23:40:44.242617+00:00"}