  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 $D_\mathsf{k}(R)$ has finite global dimension.
