The Beilinson equivalence for differential operators

[摘要] 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 (D) over tilde has a natural quotient category P(D) which imitates the category of modules on Prof of a graded commutative ring. We show that the derived category D(b)(P(D)) is equivalent to the derived category of finitely generated 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 [6] to describe the moduli space of left ideals in D. (c) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-01