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Let D be the ring of differential operators on a smooth irreducible affinevariety X over the complex numbers; or, more generally, the enveloping algebraof any locally free Lie algebroid on X. The category of finitely-generatedgraded modules of the Rees algebra D has a natural quotient category qgr(D)which imitates the category of modules on Proj of a graded commutative ring. Weshow that the derived category D^b(qgr(D)) is equivalent to the derivedcategory of finitely-generated modules of a sheaf of algebras E on X which iscoherent over X. This generalizes the usual Beilinson equivalence forprojective space, and also the Beilinson equivalence for differential operatorson a smooth curve used by Ben-Zvi and Nevins to describe the moduli space ofleft ideals in D.

The Beilinson Equivalence for Differential Operators and Lie Algebroids