{"paper":{"title":"Derived Azumaya algebras and twisted $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AT","authors_text":"Tasos Moulinos","submitted_at":"2017-10-16T16:16:24Z","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. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05810","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}