Notes on Procesi Bundles and the Symplectic Mckay Equivalence

Note that the map π is equivariant under the Gm-action, where the Gm-action on A2 is by dilation. When k is a field of positive characteristic, for simplicity, we denote A2n(1) simply by V and denote Hilb(A2)(1) by X. As has been explained in [Vain14], for any integral weight λ of G, on X there is a quantization OX , coming from quantum Hamiltonian reduction of D(g⊕ An), the sheaf of differential operators on g⊕An. For simplicity, we will denote OX by OX . Let W be the Weyl algebra on the vector space An. The ring of global sections of OX is isomorphic to WSn . We have already seen in [Vain14] that OX is an Azumaya algebra on X. We will show that RΓ : D(CohOX)→ D(ModWn)