JournalsjncgVol. 9, No. 1pp. 21–34

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
Non-commutative resolutions and Grothendieck groups cover
Download PDF

Abstract

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