{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:W5P5DAITZBUVPF2RE6EIXHB577","short_pith_number":"pith:W5P5DAIT","schema_version":"1.0","canonical_sha256":"b75fd18113c86957975127888b9c3dffde0abdee0b1c87206bf890d759a697f9","source":{"kind":"arxiv","id":"1501.00709","version":1},"attestation_state":"computed","paper":{"title":"On standard derived equivalences of orbit categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RT","authors_text":"Alexandra Zvonareva, Yury Volkov","submitted_at":"2015-01-04T19:29:29Z","abstract_excerpt":"Let $\\kk$ be a commutative ring, $\\AAA$ and $\\BB$ -- two $\\kk$-linear categories with an action of a group $G$. We introduce the notion of a standard $G$-equivalence from $\\Kb\\BB$ to $\\Kb\\AAA$. We construct a map from the set of standard $G$-equivalences to the set of standard equivalences from $\\Kb\\BB$ to $\\Kb\\AAA$ and a map from the set of standard $G$-equivalences from $\\Kb\\BB$ to $\\Kb\\AAA$ to the set of standard equivalences from $\\Kb(\\BB/G)$ to $\\Kb(\\AAA/G)$. We investigate the properties of these maps and apply our results to the case where $\\AAA=\\BB=R$ is a Frobenius $\\kk$-algebra and $"},"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":"1501.00709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-04T19:29:29Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"726f81bac416f86218601129c999a043193e1e2d18c81dc39ff660f18ac2b44f","abstract_canon_sha256":"b3c1c1ebed76682628d036a97256969a909da85c50d8a1f4f96675298a550eb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:01.967001Z","signature_b64":"sQA1Pgqs8KKFx+ykBoF/ohp/JZaMlGrZqWtebWzhRQiviMTewHpiX8weO4qpBqTGS3euYLBARm31tTUyJrVYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b75fd18113c86957975127888b9c3dffde0abdee0b1c87206bf890d759a697f9","last_reissued_at":"2026-05-18T02:30:01.966631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:01.966631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On standard derived equivalences of orbit categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RT","authors_text":"Alexandra Zvonareva, Yury Volkov","submitted_at":"2015-01-04T19:29:29Z","abstract_excerpt":"Let $\\kk$ be a commutative ring, $\\AAA$ and $\\BB$ -- two $\\kk$-linear categories with an action of a group $G$. We introduce the notion of a standard $G$-equivalence from $\\Kb\\BB$ to $\\Kb\\AAA$. We construct a map from the set of standard $G$-equivalences to the set of standard equivalences from $\\Kb\\BB$ to $\\Kb\\AAA$ and a map from the set of standard $G$-equivalences from $\\Kb\\BB$ to $\\Kb\\AAA$ to the set of standard equivalences from $\\Kb(\\BB/G)$ to $\\Kb(\\AAA/G)$. We investigate the properties of these maps and apply our results to the case where $\\AAA=\\BB=R$ is a Frobenius $\\kk$-algebra and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00709","kind":"arxiv","version":1},"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":"1501.00709","created_at":"2026-05-18T02:30:01.966688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00709v1","created_at":"2026-05-18T02:30:01.966688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00709","created_at":"2026-05-18T02:30:01.966688+00:00"},{"alias_kind":"pith_short_12","alias_value":"W5P5DAITZBUV","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"W5P5DAITZBUVPF2R","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"W5P5DAIT","created_at":"2026-05-18T12:29:47.479230+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/W5P5DAITZBUVPF2RE6EIXHB577","json":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577.json","graph_json":"https://pith.science/api/pith-number/W5P5DAITZBUVPF2RE6EIXHB577/graph.json","events_json":"https://pith.science/api/pith-number/W5P5DAITZBUVPF2RE6EIXHB577/events.json","paper":"https://pith.science/paper/W5P5DAIT"},"agent_actions":{"view_html":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577","download_json":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577.json","view_paper":"https://pith.science/paper/W5P5DAIT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00709&json=true","fetch_graph":"https://pith.science/api/pith-number/W5P5DAITZBUVPF2RE6EIXHB577/graph.json","fetch_events":"https://pith.science/api/pith-number/W5P5DAITZBUVPF2RE6EIXHB577/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577/action/storage_attestation","attest_author":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577/action/author_attestation","sign_citation":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577/action/citation_signature","submit_replication":"https://pith.science/pith/W5P5DAITZBUVPF2RE6EIXHB577/action/replication_record"}},"created_at":"2026-05-18T02:30:01.966688+00:00","updated_at":"2026-05-18T02:30:01.966688+00:00"}