2003/01/28 by Amnon Yekutieli, Yekutieli, Amnon, James J. Zhang +1
Mathematics · #16S32 #16U20 #16W70 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 16D90 #Rings and Algebras (math.RA) #Secondary: 18G10 #math.AG #math.RA #msc:16D90 #msc:16S32 #msc:16U20 #msc:16W70 #msc:18G10
paper · pdf · doi:10.48550/arxiv.math/0301323
38 pages; minor changes; final version, to appear in Compositio Math
arxiv created 2004/07/14 · arxiv updated 2009/11/30
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.