Dualizing complexes and perverse sheaves on noncommutative ringed schemes

Amnon Yekutieli, James J. Zhang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A quasi-coherent ringed scheme is a pair (X, script A sign ), where X is a scheme, and script A sign is a noncomutative quasi-coherent script O sign x-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated differential quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex. In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into a global complex.

Original languageEnglish
Pages (from-to)137-177
Number of pages41
JournalSelecta Mathematica, New Series
Volume12
Issue number1
DOIs
StatePublished - 1 Jun 2006

Keywords

  • Dualizing complexes
  • Noncommutative algebraic geometry
  • Perverse sheaves

ASJC Scopus subject areas

  • Mathematics (all)
  • Physics and Astronomy (all)

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