# The derived category of a GIT quotient

@article{HalpernLeistner2012TheDC, title={The derived category of a GIT quotient}, author={Daniel Halpern-Leistner}, journal={arXiv: Algebraic Geometry}, year={2012} }

Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory quotient. This generalizes classical descriptions of the category of coherent sheaves on projective space and categorifies several results in the theory of Hamiltonian group actions on projective manifolds.
This perspective generalizes and provides new insight into examples of derived equivalences…

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