Generalised Hasse-Schmidt varieties and their jet spaces
Algebraic Geometry
2014-02-26 v2 Commutative Algebra
Logic
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.
Cite
@article{arxiv.0908.4230,
title = {Generalised Hasse-Schmidt varieties and their jet spaces},
author = {Rahim Moosa and Thomas Scanlon},
journal= {arXiv preprint arXiv:0908.4230},
year = {2014}
}
Comments
This significantly revised version is to appear in the Proceedings of the London Mathematical Society