Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2002

Preprint Number 2002

Previous Next Preprint server

2002. Ivan Tomasic and Michael Wibmer
Difference Galois theory and dynamics

Submission date: 9 June 2021


We develop a Galois theory for difference ring extensions, inspired by Magid's separable Galois theory for ring extensions and by Janelidze's categorical Galois theory. Our difference Galois theorem states that the category of difference ring extensions split by a chosen Galois difference ring extension is classified by actions of the associated difference profinite Galois groupoid. In particular, difference locally étale extensions of a difference ring are classified by its difference profinite fundamental groupoid.
The emergence of difference profinite spaces, viewed as discrete dynamical systems in the realm of topological dynamics, leads us to investigate the interaction of difference algebra and symbolic dynamics. As an application of this interaction, we prove the near-rationality of a certain difference zeta function counting solutions of systems of difference algebraic equations over algebraic closures of finite fields with Frobenius.

Mathematics Subject Classification: 18E50, 12H05, 37B10, 18D40

Keywords and phrases:

Full text: pdf, dvi, ps.

Last updated: June 16 2021 09:52 Please send your corrections to: