Seminar

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For an orbifold X arising as the GIT quotient of a quasi-symmetric linear representation of a reductive group G, the fundamental group of the complement of a certain hyperplane arrangement acts on the derived category D^b_{coh}(X). Regarding this as a ``local system of categories," one can extend this structure to a perverse schober, which categorifies the notion of a perverse sheaf with singularities along the hyperplane arrangement. I will discuss a different categorical structure, involving semiorthogonal decompositions of equivariant derived categories and mutations thereof, that gives rise to this schober (and in particular the fundamental group action on D^b_{coh}(X)).