{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PT7LCTH6YI3ZNP4LL5XAV4GI7W","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":"29ec61176e842a94193f79c7156e4946030029cc7eacc6d32f5e72e6de365087","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-29T01:01:00Z","title_canon_sha256":"db16f07451c94759633fc42ab5bf568ece603d583edbaded9eaa1e6138f9fb49"},"schema_version":"1.0","source":{"id":"1604.08662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08662","created_at":"2026-05-18T01:16:03Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08662v1","created_at":"2026-05-18T01:16:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08662","created_at":"2026-05-18T01:16:03Z"},{"alias_kind":"pith_short_12","alias_value":"PT7LCTH6YI3Z","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PT7LCTH6YI3ZNP4L","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PT7LCTH6","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:2dc4eb6dbd1d7f24b749e6523c98e04e20e0169b8088267b61015442a97e5af8","target":"graph","created_at":"2026-05-18T01:16:03Z","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":"Recently, Rizzardo and Van den Bergh constructed an example of a triangulated functor between the derived categories of coherent sheaves on smooth projective varieties over a field $k$ of characteristic $0$ which is not of the Fourier-Mukai type. The purpose of this note is to show that if $char \\, k =p$ then there are very simple examples of such functors. Namely, for a smooth projective $Y$ over $\\mathbb Z_p$ with the special fiber $i: X\\hookrightarrow Y$, we consider the functor $L i^* \\circ i_*: D^b(X) \\to D^b(X)$ from the derived categories of coherent sheaves on $X$ to itself. We show th","authors_text":"Vadim Vologodsky","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-29T01:01:00Z","title":"Triangulated endofunctors of the derived category of coherent sheaves which do not admit DG liftings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08662","kind":"arxiv","version":1},"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:b6f51fde2ff9946880daf4098d02f1b7847c588cee7a7fc3dcd6a8d9931a00f9","target":"record","created_at":"2026-05-18T01:16:03Z","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":"29ec61176e842a94193f79c7156e4946030029cc7eacc6d32f5e72e6de365087","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-29T01:01:00Z","title_canon_sha256":"db16f07451c94759633fc42ab5bf568ece603d583edbaded9eaa1e6138f9fb49"},"schema_version":"1.0","source":{"id":"1604.08662","kind":"arxiv","version":1}},"canonical_sha256":"7cfeb14cfec23796bf8b5f6e0af0c8fdafe0e593ce9eb0e88939cca0fc5c084a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cfeb14cfec23796bf8b5f6e0af0c8fdafe0e593ce9eb0e88939cca0fc5c084a","first_computed_at":"2026-05-18T01:16:03.186738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:03.186738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WNYEurYKw7uB+/aBOIpYC2di5TRWOF0se2G6B5AJ/CI64t5DUkNJOXUhc2ctTSN6EhBPhm/pzhwY8r5tgQgdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:03.187369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6f51fde2ff9946880daf4098d02f1b7847c588cee7a7fc3dcd6a8d9931a00f9","sha256:2dc4eb6dbd1d7f24b749e6523c98e04e20e0169b8088267b61015442a97e5af8"],"state_sha256":"f70e95887d4c6eec9afa1ef8bafde09c4ed3ea96d61cb0e97a0bdd4a0e474219"}