{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4F4WU2MUWIRLWRJRO4J665IMM3","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":"047f1063012f2cc4cf31eed3faccaa82e3f0538559040448ba49b591fbc945bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-16T10:45:04Z","title_canon_sha256":"063923a66fc48f42d02894b2cc4d5c7d559c5589598754fdc901e9207860ac05"},"schema_version":"1.0","source":{"id":"1309.3893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3893","created_at":"2026-05-18T01:36:22Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3893v2","created_at":"2026-05-18T01:36:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3893","created_at":"2026-05-18T01:36:22Z"},{"alias_kind":"pith_short_12","alias_value":"4F4WU2MUWIRL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4F4WU2MUWIRLWRJR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4F4WU2MU","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:41ebe4dd8cb169858620f50469b75bbe3450b154f00c5c541381f8190a63dbea","target":"graph","created_at":"2026-05-18T01:36:22Z","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":"Let $X$ be flat scheme over $\\mathbb{Z}$ such that its base change, $X_p$, to $\\bar{\\mathbb{F}}_p$ is Frobenius split for all primes $p$. Let $G$ be a reductive group scheme over $\\mathbb{Z}$ acting on $X$. In this paper, we prove a result on the $N_p$ property for line bundles on GIT quotients of $X_{\\mathbb{C}}$ for the action of $G_{\\mathbb{C}}$. We apply our result to the special cases of (1) an action of a finite group on the projective space and (2) the action of a maximal torus on the flag variety of type $A_n$.","authors_text":"Krishna Hanumanthu, S. Senthamarai Kannan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-16T10:45:04Z","title":"Syzygies of some GIT quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3893","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:ff50e6d9a19f53454925e1797d0534eb2d24a4681d6f7cc5d3c012611a565d76","target":"record","created_at":"2026-05-18T01:36:22Z","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":"047f1063012f2cc4cf31eed3faccaa82e3f0538559040448ba49b591fbc945bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-16T10:45:04Z","title_canon_sha256":"063923a66fc48f42d02894b2cc4d5c7d559c5589598754fdc901e9207860ac05"},"schema_version":"1.0","source":{"id":"1309.3893","kind":"arxiv","version":2}},"canonical_sha256":"e1796a6994b222bb45317713ef750c66daf315fc9988bdd9a989ca5ba1bf0c81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1796a6994b222bb45317713ef750c66daf315fc9988bdd9a989ca5ba1bf0c81","first_computed_at":"2026-05-18T01:36:22.998214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:22.998214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hru6rmq/nfoql3oqJAFXGu+0SAuOARt1MwN07YJ9lMj1CGtGVDVJejnC0MPS84lebUgd3gWpDHTrDpTSVO95BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:22.998778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff50e6d9a19f53454925e1797d0534eb2d24a4681d6f7cc5d3c012611a565d76","sha256:41ebe4dd8cb169858620f50469b75bbe3450b154f00c5c541381f8190a63dbea"],"state_sha256":"0d83c12a417c234ad27bdf731136999cd4d0716c653c269d8938788f09b5e8f3"}