{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4ZEDWIF3F5PKTDGPFQHA6GD5AL","short_pith_number":"pith:4ZEDWIF3","schema_version":"1.0","canonical_sha256":"e6483b20bb2f5ea98ccf2c0e0f187d02fcbecfd97ae14218e2ba966168f938a2","source":{"kind":"arxiv","id":"1302.5289","version":2},"attestation_state":"computed","paper":{"title":"Global Jacquet-Langlands correspondence for division algebras in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"A.I.Badulescu, Ph.Roche","submitted_at":"2013-02-21T14:21:37Z","abstract_excerpt":"We prove a full global Jacquet-Langlands correspondence between GL(n) and division algebras over global fields of non zero characteristic. If $D$ is a central division algebra of dimension $n^2$ over a global field $F$ of non zero characteristic, we prove that there exists an injective map from the set of automorphic square integrable representations of the multiplicative group of $D$ to the set of automorphic square integrable representations of GL_n(F), compatible at all places with the local Jacquet-Langlands correspondence for unitary representations. We characterize the image of the map. "},"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":"1302.5289","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-21T14:21:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"083214a776421befa7b3540c3b20fead3fd638551b586381c3a1c4a7c043052e","abstract_canon_sha256":"25572594399565e3954718673be40d3b4d5a5701df7bafcf65c770649b6077ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:41.299520Z","signature_b64":"xcMJltU7KR4QbP+z877B8HsHSheBrdGvPliA9yFzZPZwHxiXSHRp8bz2s/W9LpRV6MA+87GAgUlu1YqX4JtFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6483b20bb2f5ea98ccf2c0e0f187d02fcbecfd97ae14218e2ba966168f938a2","last_reissued_at":"2026-05-18T02:47:41.298624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:41.298624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Jacquet-Langlands correspondence for division algebras in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"A.I.Badulescu, Ph.Roche","submitted_at":"2013-02-21T14:21:37Z","abstract_excerpt":"We prove a full global Jacquet-Langlands correspondence between GL(n) and division algebras over global fields of non zero characteristic. If $D$ is a central division algebra of dimension $n^2$ over a global field $F$ of non zero characteristic, we prove that there exists an injective map from the set of automorphic square integrable representations of the multiplicative group of $D$ to the set of automorphic square integrable representations of GL_n(F), compatible at all places with the local Jacquet-Langlands correspondence for unitary representations. We characterize the image of the map. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5289","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":"1302.5289","created_at":"2026-05-18T02:47:41.298774+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5289v2","created_at":"2026-05-18T02:47:41.298774+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5289","created_at":"2026-05-18T02:47:41.298774+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZEDWIF3F5PK","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZEDWIF3F5PKTDGP","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZEDWIF3","created_at":"2026-05-18T12:27:34.582898+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/4ZEDWIF3F5PKTDGPFQHA6GD5AL","json":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL.json","graph_json":"https://pith.science/api/pith-number/4ZEDWIF3F5PKTDGPFQHA6GD5AL/graph.json","events_json":"https://pith.science/api/pith-number/4ZEDWIF3F5PKTDGPFQHA6GD5AL/events.json","paper":"https://pith.science/paper/4ZEDWIF3"},"agent_actions":{"view_html":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL","download_json":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL.json","view_paper":"https://pith.science/paper/4ZEDWIF3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5289&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZEDWIF3F5PKTDGPFQHA6GD5AL/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZEDWIF3F5PKTDGPFQHA6GD5AL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL/action/storage_attestation","attest_author":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL/action/author_attestation","sign_citation":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL/action/citation_signature","submit_replication":"https://pith.science/pith/4ZEDWIF3F5PKTDGPFQHA6GD5AL/action/replication_record"}},"created_at":"2026-05-18T02:47:41.298774+00:00","updated_at":"2026-05-18T02:47:41.298774+00:00"}