Generators and defining relations for the ring of differential operators on a smooth affine algebraic variety in prime characteristic

Abstract

For the ring of differential operators D ( O ( X ) ) on a smooth affine algebraic variety X over a perfect field of characteristic p > 0 , explicit algebra generators and defining relations are found. A finite set of generators and a finite set of defining relations are given explicitly for the module Der K ( O ( X ) ) of derivations on the algebra O ( X ) of regular functions on the variety X.