On direct and inverse images of \(\mathcal D\)-modules in prime characteristic (Q1120629)

The paper studies the category of modules over the ring of algebraic differential operators on algebraic varieties over a field with finite characteristic. Generalizing the characteristic zero construction, the author defines the functors of direct and inverse images for \({\mathcal D}\)- modules with respect to a morphism \(f:\quad X\to Y\) of smooth varieties. As in the case of characteristic zero, tensoring with the canonical module yields an equivalence between the categories of left and right \({\mathcal D}\)-modules. Finally, an analogy of Kashiwara's equivalence in characteristic \(\neq 0\) is proved, which describes \({\mathcal D}\)-modules with support on a closed subvariety.