Derived localization (joint with J. Chuang and C. Braun)

Andrey Lazarev (University of Lancaster)

Wednesday 14th January, 2015 16:00-17:00 Maths 516


Localization of commutative rings and modules is a basic procedure in commutative algebra; one of its main properties is exactness. This property allows easily to define the corresponding notion on the level of homotopy categories. Noncommutative localization is much harder, but also much more interesting. It comes up in various contexts, e.g. the construction of a derived category could be viewed as localization with respect to quasi-isomorphism.

 I will explain how to construct noncommutative localization in so that exactness is preserved. Applications include generalized group completion theorem, cyclic homology of algebras, graph homology and others.

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