{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I5IJEJIIHW5WEKUOZC6DWSX5ZL","short_pith_number":"pith:I5IJEJII","schema_version":"1.0","canonical_sha256":"47509225083dbb622a8ec8bc3b4afdcacab1cb07af9e6d2111dd82819052101b","source":{"kind":"arxiv","id":"1110.5707","version":4},"attestation_state":"computed","paper":{"title":"Quantum geometric Langlands correspondence in positive characteristic: the GL(N) case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"Roman Travkin","submitted_at":"2011-10-26T06:04:52Z","abstract_excerpt":"We prove a version of quantum geometric Langlands conjecture in characteristic $p$. Namely, we construct an equivalence of certain localizations of derived categories of twisted crystalline $\\mathcal D$-modules on the stack of rank $N$ vector bundles on an algebraic curve $C$ in characteristic $p$. The twisting parameters are related in the way predicted by the conjecture, and are assumed to be irrational (i.e., not in $\\mathbb F_p$). We thus extend the results of arXiv:math/0602255 concerning the similar problem for the usual (non-quantum) geometric Langlands.\n  In the course of the proof, we"},"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":"1110.5707","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-26T06:04:52Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"c470a13bc3cc51f89296d2d1b0e1916fe651b81c8f1efc86424d7f788eb7fcd2","abstract_canon_sha256":"45dfd6ea5d817f65d8b56ac73957a2464a436e2044bc97d057cad6cef6d01867"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:53.425527Z","signature_b64":"/13WxI4rWbYDmAo+mm5TNIcig2YXZgS0FGT0elBArXt+eWCv63Vy+7lLlC6wRh6vXID2tbakt0HfeatXTH6TDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47509225083dbb622a8ec8bc3b4afdcacab1cb07af9e6d2111dd82819052101b","last_reissued_at":"2026-05-18T01:12:53.425082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:53.425082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum geometric Langlands correspondence in positive characteristic: the GL(N) case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"Roman Travkin","submitted_at":"2011-10-26T06:04:52Z","abstract_excerpt":"We prove a version of quantum geometric Langlands conjecture in characteristic $p$. Namely, we construct an equivalence of certain localizations of derived categories of twisted crystalline $\\mathcal D$-modules on the stack of rank $N$ vector bundles on an algebraic curve $C$ in characteristic $p$. The twisting parameters are related in the way predicted by the conjecture, and are assumed to be irrational (i.e., not in $\\mathbb F_p$). We thus extend the results of arXiv:math/0602255 concerning the similar problem for the usual (non-quantum) geometric Langlands.\n  In the course of the proof, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5707","kind":"arxiv","version":4},"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":"1110.5707","created_at":"2026-05-18T01:12:53.425136+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.5707v4","created_at":"2026-05-18T01:12:53.425136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5707","created_at":"2026-05-18T01:12:53.425136+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5IJEJIIHW5W","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5IJEJIIHW5WEKUO","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5IJEJII","created_at":"2026-05-18T12:26:30.835961+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/I5IJEJIIHW5WEKUOZC6DWSX5ZL","json":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL.json","graph_json":"https://pith.science/api/pith-number/I5IJEJIIHW5WEKUOZC6DWSX5ZL/graph.json","events_json":"https://pith.science/api/pith-number/I5IJEJIIHW5WEKUOZC6DWSX5ZL/events.json","paper":"https://pith.science/paper/I5IJEJII"},"agent_actions":{"view_html":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL","download_json":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL.json","view_paper":"https://pith.science/paper/I5IJEJII","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.5707&json=true","fetch_graph":"https://pith.science/api/pith-number/I5IJEJIIHW5WEKUOZC6DWSX5ZL/graph.json","fetch_events":"https://pith.science/api/pith-number/I5IJEJIIHW5WEKUOZC6DWSX5ZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL/action/storage_attestation","attest_author":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL/action/author_attestation","sign_citation":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL/action/citation_signature","submit_replication":"https://pith.science/pith/I5IJEJIIHW5WEKUOZC6DWSX5ZL/action/replication_record"}},"created_at":"2026-05-18T01:12:53.425136+00:00","updated_at":"2026-05-18T01:12:53.425136+00:00"}