Non-commutative resolutions and Grothendieck groups
By Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial. 2012
48 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e71808b4c505b4f21c63bb5b784858c6f74de3f6
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Relative singularity categories I: Auslander resolutions (2012, background): “If gldim(A) ∞ then A is called a non-commutative resolution (NCR) of R (cf. [31]).”
- Non-commutative resolutions of quotient singularities for reductive groups (2015, unknown): “educible G-representations by Gb. 1.1. Preliminaries on non-commutative resolutions. We first recall the defi- nition of a non-commutative (crepant) resolution (abbreviated as NC(C)R). Definition 1.1.1. [15, 40, 60, 63] Assume that S is a normal noetherian domain. Then a non-commutative resolution of S”