{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TFHQH4MPTJLLJUQ4RV3RCFHYHP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"20256e4125c8a51635a8fcd606b392073f8c92af9b424a9c486cd2c721ddf055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-19T18:29:34Z","title_canon_sha256":"a127baf3fb7728c0e4e0129cb7a979b856ef2461283e072c636964dc18ed084c"},"schema_version":"1.0","source":{"id":"1107.3798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3798","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3798v1","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3798","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"TFHQH4MPTJLL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TFHQH4MPTJLLJUQ4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TFHQH4MP","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:ac50f61a311a720849bddc8bd7938698751d7a52f97c7d16ac77d5a67fdb0688","target":"graph","created_at":"2026-05-18T04:17:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In 1960 Borel proved a \"localization\" result relating the rational cohomology of a topological space X to the rational cohomology of the fixed points for a torus action on X. This result and its generalizations have many applications in Lie theory. In 1934, P. Smith proved a similar localization result relating the mod p cohomology of X to the mod p cohomology of the fixed points for a Z/p-action on X. In this paper we study Z/p-localization (\"Smith theory\") for constructible sheaves and functions. We show that Smith theory on loop groups is related via the geometric Satake correspondence to s","authors_text":"David Treumann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-19T18:29:34Z","title":"Smith theory and geometric Hecke algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3798","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:00cc8b0aea2ae2bd5edcac9f5fb636599d1330ada512dc483619932f9d3c94f3","target":"record","created_at":"2026-05-18T04:17:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"20256e4125c8a51635a8fcd606b392073f8c92af9b424a9c486cd2c721ddf055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-19T18:29:34Z","title_canon_sha256":"a127baf3fb7728c0e4e0129cb7a979b856ef2461283e072c636964dc18ed084c"},"schema_version":"1.0","source":{"id":"1107.3798","kind":"arxiv","version":1}},"canonical_sha256":"994f03f18f9a56b4d21c8d771114f83befdb1b3610252e25fd2e642c93c9d15b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"994f03f18f9a56b4d21c8d771114f83befdb1b3610252e25fd2e642c93c9d15b","first_computed_at":"2026-05-18T04:17:15.920383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:15.920383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VnbXGye7bbeIQ7cR/gDrsQDrsUEVB4wqLcWFns/OSiymPNJ4jgfmDXfhwRfwX341Vrwy4dhba4ErQeRlHx9rBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:15.921079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00cc8b0aea2ae2bd5edcac9f5fb636599d1330ada512dc483619932f9d3c94f3","sha256:ac50f61a311a720849bddc8bd7938698751d7a52f97c7d16ac77d5a67fdb0688"],"state_sha256":"4e07efe5851c02f64b25380fb9fa0a6ebab25f7e94b12f0724aeb1e1da2ce6da"}