# Non-Commutative Resolutions of Toric Varieties

@inproceedings{Faber2018NonCommutativeRO, title={Non-Commutative Resolutions of Toric Varieties}, author={Eleonore Faber and Greg Muller and Karen E. Smith}, year={2018} }

Let $R$ be the coordinate ring of an affine toric variety. We show that the endomorphism ring $End_R(\mathbb A),$ where $\mathbb A$ is the (finite) direct sum of all (isomorphism classes of) conic $R$-modules, has finite global dimension. Furthermore, we show that $End_R(\mathbb A)$ is a non-commutative crepant resolution if and only if the toric variety is simplicial. For toric varieties over a perfect field $k$ of prime characteristic, we show that the ring of differential operators $D_… CONTINUE READING

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