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arXiv · 1205.4486

Non-commutative resolutions and Grothendieck groups

Hailong Dao·Osamu Iyama·Ryo Takahashi·Charles Vial
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Abstract

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

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Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial. 2012-05-21. Non-commutative resolutions and Grothendieck groups. https://arxiv.org/abs/1205.4486

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