Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms

Takehiko Yasuda

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The aim of this paper is threefold: first, to prove that the endomorphism ring associated to a pure subring of a regular local ring is a noncommutative crepant resolution if it is maximal Cohen-Macaulay; second, to see that in that situation, a different, but Morita equivalent, noncommutative crepant resolution can be constructed by using Frobenius morphisms; finally, to study the relation between Frobenius morphisms of noncommutative rings and the finiteness of global dimension. As a byproduct, we will obtain a result on wild quotient singularities: If the smooth cover of a wild quotient singularity is unramified in codimension one, then the singularity is not strongly F-regular.

Original languageEnglish
Pages (from-to)15-31
Number of pages17
JournalJournal of Algebra
Volume370
DOIs
Publication statusPublished - 2012 Nov 15

Keywords

  • Cohen-Macaulay modules
  • Endomorphism rings
  • Frobenius morphisms
  • Global dimension
  • Noncommutative crepant resolutions
  • Quotient singularities
  • Skew group rings

ASJC Scopus subject areas

  • Algebra and Number Theory

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