{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LEQYWK77SSR75EQPO5AWFP27GN","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":"74ba347aeb2143c37ce32d3f030984d2621320d15e56c7476500dda268474c27","cross_cats_sorted":["math.AG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-16T16:16:24Z","title_canon_sha256":"4c81fc5b23562f957fab17b710e353f164dbb133a590e305e01fd7d3ed2fc5c4"},"schema_version":"1.0","source":{"id":"1710.05810","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05810","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05810v2","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05810","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"LEQYWK77SSR7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LEQYWK77SSR75EQP","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LEQYWK77","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:f4d8db29d4f96c8433d5b93f8ed9825f5d1f207e3b52666804104aaa9e49bcd2","target":"graph","created_at":"2026-05-17T23:47:49Z","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":"We construct a relative version of topological $K$-theory of dg categories over an arbitrary quasi-compact, quasi-separated $\\mathbb{C}$-scheme $X$. This has as input a $\\text{Perf}(X)$-linear stable $\\infty$-category and output a sheaf of spectra on $X(\\mathbb{C})$, the space of complex points of $X$. We then characterize the values of this functor on inputs of the form $Mod_{A}^{\\omega}$, for $A$ a derived Azumaya algebra over $X$. In such cases we show that this coincides with the $\\alpha$-twisted topological $K$-theory of $X(\\mathbb{C})$ for some appropriately defined twist of $K$-theory. ","authors_text":"Tasos Moulinos","cross_cats":["math.AG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-16T16:16:24Z","title":"Derived Azumaya algebras and twisted $K$-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05810","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":"sha256:03d149a1933cdba3b7ab051029a7fe7d2fed61f8f8e2fd356f78e443ca9f1f5f","target":"record","created_at":"2026-05-17T23:47:49Z","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":"74ba347aeb2143c37ce32d3f030984d2621320d15e56c7476500dda268474c27","cross_cats_sorted":["math.AG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-16T16:16:24Z","title_canon_sha256":"4c81fc5b23562f957fab17b710e353f164dbb133a590e305e01fd7d3ed2fc5c4"},"schema_version":"1.0","source":{"id":"1710.05810","kind":"arxiv","version":2}},"canonical_sha256":"59218b2bff94a3fe920f774162bf5f33515a413282232fe53db69ca5fdf0984f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59218b2bff94a3fe920f774162bf5f33515a413282232fe53db69ca5fdf0984f","first_computed_at":"2026-05-17T23:47:49.215596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:49.215596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/7XA2yUA5+Ah0vGAFrKX2PlJqVk1m771itmBGwy35yi9te2GfON2avUEnNPhlOsfaxFFFA90yq7pn7YLEXXCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:49.216216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05810","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03d149a1933cdba3b7ab051029a7fe7d2fed61f8f8e2fd356f78e443ca9f1f5f","sha256:f4d8db29d4f96c8433d5b93f8ed9825f5d1f207e3b52666804104aaa9e49bcd2"],"state_sha256":"1f32cb0b9bb6ad3c5e7fd3c07e5a991577f81415dcd402310b4e840ad7e2fd55"}