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

TL;DR

This paper explicitly determines generators and defining relations for the ring of differential operators on smooth affine algebraic varieties over perfect fields of prime characteristic.

Contribution

It provides an explicit description of generators and relations for differential operator rings in prime characteristic, advancing algebraic understanding.

Findings

Explicit generators for differential operator rings are identified.

Defining relations among generators are explicitly described.

Results apply to smooth affine algebraic varieties over perfect fields.

Abstract

For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.