Submission date: 30 August 2016

Abstract:

[Contains an erratum to [4] (Z. Chatzidakis, E. Hrushovski, Y. Peterzil, Model theory of difference fields, II: Periodic ideals and the trichotomy in all characteristics, Proceedings of the London Math. Society(3) 85 (2002), 257 - 311)]
The main idea of [4] was that structures built from periodic prime ideals have better properties from the usual ones built from invariant ideals; but unable to work with periodic ideals alone, we had to generalise further to a somewhat ephemeral setting called virtual ideals. This text has two purposes. It corrects an error in [4] discovered by Tom Scanlon's UCB seminar, recovering all results for all virtual ideals. In addition, based on results in [3], we describe a wide family of difference equations where virtual ideals reduce to periodic ideals.

Mathematics Subject Classification: 03C60, 12H10

Keywords and phrases: difference fields, trichotomy, Zariski geometries.

Full text arXiv 1608.08438: pdf, ps.