The Beilinson Equivalence for Differential Operators and Lie Algebroids
نویسنده
چکیده
Let D be the ring of differential operators on a smooth irreducible affine variety X over C; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded modules of the Rees algebra e D has a natural quotient category qgr( e D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived category D(qgr( e D)) is equivalent to the derived category of finitelygenerated modules of a sheaf of algebras E on X which is coherent over X. This generalizes the usual Beilinson equivalence for projective space, and also the Beilinson equivalence for differential operators on a smooth curve used by Ben-Zvi and Nevins in [4] to describe the moduli space of left ideals in D.
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