Derived Azumaya algebras and twisted $K$-theory

@article{Moulinos2017DerivedAA,
  title={Derived Azumaya algebras and twisted \$K\$-theory},
  author={Tasos Moulinos},
  journal={arXiv: Algebraic Topology},
  year={2017},
  pages={761-803}
}
  • Tasos Moulinos
  • Published 2017
  • Mathematics
  • arXiv: Algebraic Topology
  • 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… CONTINUE READING

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