Dimension Polynomials for Affine Partial Difference Algebraic Groups
Algebraic Geometry
2026-05-08 v2 Commutative Algebra
Abstract
We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference ideal, and this result allows us to prove the existence of a dimension polynomial for any partial difference algebraic group.
Cite
@article{arxiv.2511.20350,
title = {Dimension Polynomials for Affine Partial Difference Algebraic Groups},
author = {Orla McGrath},
journal= {arXiv preprint arXiv:2511.20350},
year = {2026}
}
Comments
38 pages, to appear in IMRN