  Let X be a smooth toric variety. David Cox introduced the homogeneous
coordinate ring S of X and its irrelevant ideal B. Extending well-known results
on projective space, Cox established the following: (1) the category of
quasi-coherent sheaves on X is equivalent to the category of graded S-modules
modulo B-torsion, (2) the variety X is a geometric quotient of Spec(S) V(B) by
a suitable torus action. We provide the D-module version of these results. More
specifically, let A denote the ring of differential operators on Spec(S). We
show that the category of D-modules on X is equivalent to a subcategory of
graded A-modules modulo B-torsion. Additionally, we prove that the
characteristic variety of a D-module is a geometric quotient of an open subset
of the characteristic variety of the associated A-module and that holonomic
D-modules correspond to holonomic A-modules.
