{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SQXGQ2NXBJ6ODWRIY65ASVPE7J","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":"f236ab15984840eefab5d8b813f70db9858618eeb91f31f942e6a946d7e7901c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-25T16:03:10Z","title_canon_sha256":"6a0ece671fb2da70bd32c3ff38218413295c89ad5ac640d6b0528c61ebfe5228"},"schema_version":"1.0","source":{"id":"1901.08945","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08945","created_at":"2026-05-17T23:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08945v2","created_at":"2026-05-17T23:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08945","created_at":"2026-05-17T23:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"SQXGQ2NXBJ6O","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SQXGQ2NXBJ6ODWRI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SQXGQ2NX","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:27efa5d7bcb6dbcef02416c9936dfc89cbb3303e651ca693c1b89db6480156d6","target":"graph","created_at":"2026-05-17T23:53:41Z","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":"It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of complexes of sheaves with quasi-coherent cohomology. This generalizes earlier work by Lieblich for gerbes over schemes whereas our gerbes may live over arbitrary algebraic stacks.\n  By combining this decomposition with the semi-orthogonal decomposition for a projectivized vector bundle, we deduce a semi-orthogonal decomposition of the derived category of a f","authors_text":"Daniel Bergh, Olaf M. Schn\\\"urer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-25T16:03:10Z","title":"Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08945","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":"sha256:8ccdafd33ee3cf11d0286ed490b47c15ec4ecfd07b168ad51b4e2c6a4c58f776","target":"record","created_at":"2026-05-17T23:53:41Z","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":"f236ab15984840eefab5d8b813f70db9858618eeb91f31f942e6a946d7e7901c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-25T16:03:10Z","title_canon_sha256":"6a0ece671fb2da70bd32c3ff38218413295c89ad5ac640d6b0528c61ebfe5228"},"schema_version":"1.0","source":{"id":"1901.08945","kind":"arxiv","version":2}},"canonical_sha256":"942e6869b70a7ce1da28c7ba0955e4fa7267a2be03131ee5980cd28090f09e14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"942e6869b70a7ce1da28c7ba0955e4fa7267a2be03131ee5980cd28090f09e14","first_computed_at":"2026-05-17T23:53:41.103910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:41.103910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZ/wxHmpabaFZ54EAPXjl2S2+2k4qPtwSaX8RHw2Df6xZ5TVO3xso8gMVTC+WILh0sx6KXLe0iYrTdMaQjuGBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:41.104329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.08945","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ccdafd33ee3cf11d0286ed490b47c15ec4ecfd07b168ad51b4e2c6a4c58f776","sha256:27efa5d7bcb6dbcef02416c9936dfc89cbb3303e651ca693c1b89db6480156d6"],"state_sha256":"2f8b459c422b4063dc578a53daa8dac2f0ac2878118bcb3af4057e990afe97df"}