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arXiv · 0908.3662

The Beilinson Equivalence for Differential Operators and Lie Algebroids

Greg Muller
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Abstract

Let D be the ring of differential operators on a smooth irreducible affine variety X over the complex numbers; 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 has a natural quotient category qgr(D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived category D^b(qgr(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 to describe the moduli space of left ideals in D.

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Greg Muller. 2009-08-25. The Beilinson Equivalence for Differential Operators and Lie Algebroids. https://doi.org/10.1016/j.jpaa.2010.02.016

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