Non-commutative resolutions and Grothendieck groups

  • Hailong Dao

    University of Kansas, Lawrence, USA
  • Osamu Iyama

    Nagoya University, Japan
  • Ryo Takahashi

    Nagoya University, Japan
  • Charles Vial

    University of Cambridge, UK

Abstract

Let be a noetherian normal domain. We investigate when admits a faithful module whose endomorphism ring has finite global dimension. This can be viewed as a noncommutative desingularization of Spec(). We show that the existence of such modules forces stringent conditions on the Grothendieck group of finitely generated modules over . In some cases those conditions are enough to imply that Spec() has only rational singularities.

Cite this article

Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial, Non-commutative resolutions and Grothendieck groups. J. Noncommut. Geom. 9 (2015), no. 1, pp. 21–34

DOI 10.4171/JNCG/186