Serre functor on QCoh(Y) for Y = Spec A/G (G reductive, unique closed orbit) is tensoring with local cohomology of ω_Y at the orbit, yielding Matlis and local duality analogues for the stack.
Springer Berlin,3edition, March1994
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Serre functors and local duality for affine quotients
Serre functor on QCoh(Y) for Y = Spec A/G (G reductive, unique closed orbit) is tensoring with local cohomology of ω_Y at the orbit, yielding Matlis and local duality analogues for the stack.