|XXXIV Workshop on Geometric Methods in Physics||28.06-4.07.2015|
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Derived localization and infinity local systems
Localization of rings and modules is one of the basic tools in commutative algebra. In contrast, localizing noncommutative rings is a much more delicate procedure, primarily because of the non-exactness of the corresponding functor. I will show how to construct localization in a noncommutative context in such a way that exactness is manifestly present. As an application, I will describe a higher, or topological, form of the Riemann-Hilbert correspondence (recall that the classical Riemann-Hilbert correspondence is an equivalence of categories between local systems on a manifold and flat vector bundles).