{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YFYILAYZIURJHQTOSJRR55IKVI","short_pith_number":"pith:YFYILAYZ","schema_version":"1.0","canonical_sha256":"c170858319452293c26e92631ef50aaa3a6cf959f6bbd703935bb051a56b5990","source":{"kind":"arxiv","id":"1112.6340","version":4},"attestation_state":"computed","paper":{"title":"Geometry of second adjointness for p-adic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Kazhdan, Roman Bezrukavnikov","submitted_at":"2011-12-29T16:08:21Z","abstract_excerpt":"We present a geometric proof of Bernstein's second adjointness for a reductive $p$-adic group. Our approach is based on geometry of the wonderful compactification and related varieties. Considering asymptotic behavior of a function on the group in a neighborhood of a boundary stratum of the compactification, we get a \"co-specialization\" map between spaces of functions on various varieties with $G\\times G$ action. These maps can be viewed as maps of bimodules for the Hecke algebra, and the corresponding natural transformations of functors lead to the second adjointness. We also get a formula fo"},"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":"1112.6340","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-29T16:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"2c00c28f4394c4d9388bdba2d3c1b483a6d56e3b08f8fa165c7706fced075a9b","abstract_canon_sha256":"ae70a32e30f7593a06f4fda4dbaacd563c657cec064daf270c2e413258243777"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:12.135730Z","signature_b64":"OSHFUVDbO8LlNJzhSMH+oy+e3lyRmruSGkHVXLknFxD8dCl2s3DCkZ07nlZgx8/YZVtETMOYp5iQU1kUGNsUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c170858319452293c26e92631ef50aaa3a6cf959f6bbd703935bb051a56b5990","last_reissued_at":"2026-05-18T01:31:12.135233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:12.135233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of second adjointness for p-adic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Kazhdan, Roman Bezrukavnikov","submitted_at":"2011-12-29T16:08:21Z","abstract_excerpt":"We present a geometric proof of Bernstein's second adjointness for a reductive $p$-adic group. Our approach is based on geometry of the wonderful compactification and related varieties. Considering asymptotic behavior of a function on the group in a neighborhood of a boundary stratum of the compactification, we get a \"co-specialization\" map between spaces of functions on various varieties with $G\\times G$ action. These maps can be viewed as maps of bimodules for the Hecke algebra, and the corresponding natural transformations of functors lead to the second adjointness. We also get a formula fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6340","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":"1112.6340","created_at":"2026-05-18T01:31:12.135307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.6340v4","created_at":"2026-05-18T01:31:12.135307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6340","created_at":"2026-05-18T01:31:12.135307+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFYILAYZIURJ","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFYILAYZIURJHQTO","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFYILAYZ","created_at":"2026-05-18T12:26:47.523578+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/YFYILAYZIURJHQTOSJRR55IKVI","json":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI.json","graph_json":"https://pith.science/api/pith-number/YFYILAYZIURJHQTOSJRR55IKVI/graph.json","events_json":"https://pith.science/api/pith-number/YFYILAYZIURJHQTOSJRR55IKVI/events.json","paper":"https://pith.science/paper/YFYILAYZ"},"agent_actions":{"view_html":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI","download_json":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI.json","view_paper":"https://pith.science/paper/YFYILAYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.6340&json=true","fetch_graph":"https://pith.science/api/pith-number/YFYILAYZIURJHQTOSJRR55IKVI/graph.json","fetch_events":"https://pith.science/api/pith-number/YFYILAYZIURJHQTOSJRR55IKVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI/action/storage_attestation","attest_author":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI/action/author_attestation","sign_citation":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI/action/citation_signature","submit_replication":"https://pith.science/pith/YFYILAYZIURJHQTOSJRR55IKVI/action/replication_record"}},"created_at":"2026-05-18T01:31:12.135307+00:00","updated_at":"2026-05-18T01:31:12.135307+00:00"}