{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5IF7S77MRPZRHLS7AWMB5BG4K5","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":"e2d780a00b49fa9eacfe6dc322c3b07f49095840da38dbe0721fd8e6aff0abc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T21:59:14Z","title_canon_sha256":"3f40c1da5b0e2ecaf3804b01c40b451b888c390d525e761222be72dbdc1627a6"},"schema_version":"1.0","source":{"id":"1611.04197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04197","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04197v2","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04197","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"5IF7S77MRPZR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5IF7S77MRPZRHLS7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5IF7S77M","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:9c67f66322a78d17e2c7c6f6247257679b795582c7a48aaf39472848492ff692","target":"graph","created_at":"2026-05-17T23:53:34Z","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":"A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\\mathfrak{p}$-local and $\\mathfrak{p}$-torsion subcategories of the stable category, for each homogeneous prime ideal $\\mathfrak{p}$ in the cohomology ring of the group scheme.","authors_text":"Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T21:59:14Z","title":"Local duality for representations of finite group schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04197","kind":"arxiv","version":2},"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":"sha256:0bd0636d398746917d5435b8589b7e59c00708fb81c7514b18ba2e638259b556","target":"record","created_at":"2026-05-17T23:53:34Z","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":"e2d780a00b49fa9eacfe6dc322c3b07f49095840da38dbe0721fd8e6aff0abc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T21:59:14Z","title_canon_sha256":"3f40c1da5b0e2ecaf3804b01c40b451b888c390d525e761222be72dbdc1627a6"},"schema_version":"1.0","source":{"id":"1611.04197","kind":"arxiv","version":2}},"canonical_sha256":"ea0bf97fec8bf313ae5f05981e84dc5762c73cffd1f5db33dd5c585e56892dd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea0bf97fec8bf313ae5f05981e84dc5762c73cffd1f5db33dd5c585e56892dd1","first_computed_at":"2026-05-17T23:53:34.095398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:34.095398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QM3i/fTs8BDzzlI9p7HlFrTR8nwKdVJxFHctZhwE5h5jxMQWArSjcA0Klmheu+JDoBY3nf3ZJ603qad1j6U2Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:34.095919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bd0636d398746917d5435b8589b7e59c00708fb81c7514b18ba2e638259b556","sha256:9c67f66322a78d17e2c7c6f6247257679b795582c7a48aaf39472848492ff692"],"state_sha256":"68c1edb311edd8e2d48eb6fd621778a314250eefd11692c048db78af928cc409"}