Finiteness properties of affine difference algebraic groups

Research output: Contribution to journalArticlepeer-review

Abstract

We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the matrix entries can indeed be defined by finitely many such equations. As an application, we show that the difference ideal of all difference algebraic relations among the solutions of a linear differential equation is finitely generated.

Original languageEnglish
Pages (from-to)506-555
Number of pages50
JournalInternational mathematics research notices
Volume2022
Issue number1
Early online date2020
DOIs
Publication statusPublished - 1 Jan 2022

ASJC Scopus subject areas

  • Mathematics(all)

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