Zilber's Dichotomy for Differentially Closed Fields with an Automorphism

Abstract

The theory of difference-differential fields of characteristic zero hasa model-companion denoted byDCFA. In [2] we prove its main properties. In[3] we proved a weak version of Zilber’s dichotomy forDCFA. In this paperwe use arc spaces techniques as developed by Moosa, Pillay and Scanlon in[10] to suppress the extra hypothesis needed in [3] and prove the full Zilber’sdichotomy forDCFA, we also state how these techniques generalise to partialdifferential fields with an automorphism.