{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WVT5BEA6UXTJVBGR7LS53BGW3L","short_pith_number":"pith:WVT5BEA6","schema_version":"1.0","canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","source":{"kind":"arxiv","id":"1404.5011","version":6},"attestation_state":"computed","paper":{"title":"Categorical Bockstein sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.KT","authors_text":"Leonid Positselski","submitted_at":"2014-04-20T04:49:10Z","abstract_excerpt":"We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to recover the abelian/exact category of modular representations of a finite group from the exact category of its l-adic representations. The construction uses matrix factorizations in a nontraditional way. We obtain the Bockstein long exact sequences for the Ext groups in the exact categories produced by reduction. Our motivation comes from the theory of Artin-T"},"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":"1404.5011","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-20T04:49:10Z","cross_cats_sorted":["math.CT","math.RT"],"title_canon_sha256":"b772e085cb388f2acaee647a058219a3327d664ce9ab1126bf7237161320303e","abstract_canon_sha256":"7f118fa5a48af07a5d266a3a0e847073d10923dab53ffee239e26956586fad2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:10.963113Z","signature_b64":"umONmCujccjewholhaR54jlSHlbcUgkyvfIlo1yzpTKw21RzL49BPlt0fwYLyx4ktehxqhvYV1nhxCua6gBvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","last_reissued_at":"2026-05-18T00:01:10.962333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:10.962333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categorical Bockstein sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.KT","authors_text":"Leonid Positselski","submitted_at":"2014-04-20T04:49:10Z","abstract_excerpt":"We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to recover the abelian/exact category of modular representations of a finite group from the exact category of its l-adic representations. The construction uses matrix factorizations in a nontraditional way. We obtain the Bockstein long exact sequences for the Ext groups in the exact categories produced by reduction. Our motivation comes from the theory of Artin-T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5011","kind":"arxiv","version":6},"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":"1404.5011","created_at":"2026-05-18T00:01:10.962474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5011v6","created_at":"2026-05-18T00:01:10.962474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5011","created_at":"2026-05-18T00:01:10.962474+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVT5BEA6UXTJ","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVT5BEA6UXTJVBGR","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVT5BEA6","created_at":"2026-05-18T12:28:54.890064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.02129","citing_title":"From Diaz's Enriques Product to an $n$-Fold Cup-Product Bockstein Family of Integral Hodge Counterexamples","ref_index":52,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L","json":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L.json","graph_json":"https://pith.science/api/pith-number/WVT5BEA6UXTJVBGR7LS53BGW3L/graph.json","events_json":"https://pith.science/api/pith-number/WVT5BEA6UXTJVBGR7LS53BGW3L/events.json","paper":"https://pith.science/paper/WVT5BEA6"},"agent_actions":{"view_html":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L","download_json":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L.json","view_paper":"https://pith.science/paper/WVT5BEA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5011&json=true","fetch_graph":"https://pith.science/api/pith-number/WVT5BEA6UXTJVBGR7LS53BGW3L/graph.json","fetch_events":"https://pith.science/api/pith-number/WVT5BEA6UXTJVBGR7LS53BGW3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/action/storage_attestation","attest_author":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/action/author_attestation","sign_citation":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/action/citation_signature","submit_replication":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/action/replication_record"}},"created_at":"2026-05-18T00:01:10.962474+00:00","updated_at":"2026-05-18T00:01:10.962474+00:00"}