Derived noncommutative algebraic geometry

In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories and related constructions of triangulated categories using categorical tools. Some basic examples include the bounded derived category of coherent sheaves on a smooth variety, D b ( X ) {\displaystyle D^{b}(X)} , called its derived category, or the derived category of perfect complexes on an algebraic variety, denoted D perf ( X ) {\displaystyle D_{\operatorname {perf} }(X)} .

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