Derived localisation of algebras and modules

Joe Chuang (City)

Frank Adams 1,

Localisation of commutative rings is straightforward and well understood. Noncommutative localisation is more subtle, in part because it is not an exact functor. Andrey Lazarev, Chris Braun and I have been studying the derived localisation of a (not necessarily commutative) ring A at a subset S; it is a differential graded ring obtained from A by inverting the elements of S in a universal, homotopy invariant, way. In my talk I will describe our main theorem, that the derived category of the derived localisation is a Bousfield localisation of the derived category of A, and give some examples and applications.

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