# 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 $\alpha… CONTINUE READING #### Citations ##### Publications citing this paper. SHOWING 1-3 OF 3 CITATIONS ## Twisted Fourier-Mukai partners of Enriques surfaces • Mathematics • 2018 ## The integral Hodge conjecture for two-dimensional Calabi-Yau categories VIEW 4 EXCERPTS CITES METHODS & BACKGROUND HIGHLY INFLUENCED ## Topological K-theory of twisted equivariant perfect complexes • Mathematics • 2019 VIEW 1 EXCERPT #### References ##### Publications referenced by this paper. SHOWING 1-10 OF 33 REFERENCES ## Motivic Realizations of Matrix Factorizations and Vanishing Cycles • Mathematics • 2016 ## Descent in algebraic$K$-theory and a conjecture of Ausoni-Rognes • Mathematics • 2016 ## Derived Azumaya algebras and generators for twisted derived categories ## Topological K-theory of complex noncommutative spaces ## An ∞‐categorical approach to R‐line bundles, R‐module Thom spectra, and twisted R‐homology • Mathematics • 2014 ## A universal characterization of higher algebraic K-theory • Mathematics • 2010 ## Twisted K-theory • Mathematics • 2004 ## Higher Algebraic K-Theory of Schemes and of Derived Categories • Mathematics • 1990 ## Uniqueness of the multiplicative cyclotomic trace • Mathematics • 2011 ## Some remarks on topological$K\$-theory of dg categories

• Mathematics
• 2017