Zilber's Dichotomy for Differentially Closed Fields with an Automorphism

Abstract

The theory of difference-differential fields of characteristic zero has a model-companion denoted by $DCFA$. Previously we proved a weak version of Zilber's dichotomy for $DCFA$. In this paper we use arc spaces techniques as developed by Moosa, Pillay and Scanlon to suppress the extra hypothesis needed before and prove the full Zilber's dichotomy for $DCFA$, we also state how these techniques generalise to partial differential fields with an automorphism.