Generalized Hasse-Schmidt varieties and their jet spaces

Abstract

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally, allowing the development of the theory for arbitrary systems of algebraic partial difference/differential equations, where constructions by earlier authors applied only to the finite dimensional case. In particular, it is shown that under appropriate separability assumptions a Hasse variety is determined by its jet spaces at a point.