(previous title: Differential Algebras of Finite Type)

Abstract:

A differential algebra of finite type over a field k is a

filtered algebra A, such that the associated graded algebra is

finite over its center, and the center is a finitely generated

k-algebra. The prototypical example is the algebra of

differential operators on a smooth affine variety, when char k =

0. We study homological and geometric properties of differential

algebras of finite type. The main results concern the rigid

dualizing complex over such an algebra A: its existence,

structure and variance properties. We also define and study

perverse A-modules, and show how they are related to the

Auslander property of the rigid dualizing complex of A.

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updated 21 Feb 2006