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.
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Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial, Non-commutative resolutions and Grothendieck groups. J. Noncommut. Geom. 9 (2015), no. 1, pp. 21–34DOI 10.4171/JNCG/186