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.
Original language | English |
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Pages (from-to) | 620-654 |
Number of pages | 35 |
Journal | Compositio Mathematica |
Volume | 141 |
Issue number | 3 |
DOIs | |
State | Published - 28 Nov 2005 |
Keywords
- Dualizing complexes
- Filtered rings
- Noncommutative rings
ASJC Scopus subject areas
- Algebra and Number Theory