Dualizing complexes and perverse modules over differential algebras

Amnon Yekutieli, James J. Zhang

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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 languageEnglish
Pages (from-to)620-654
Number of pages35
JournalCompositio Mathematica
Volume141
Issue number3
DOIs
StatePublished - 28 Nov 2005

Keywords

  • Dualizing complexes
  • Filtered rings
  • Noncommutative rings

ASJC Scopus subject areas

  • Algebra and Number Theory

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