Submission date: 23 June 2020

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.

Mathematics Subject Classification: 11U09, 12H05, 12H10

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Full text arXiv 2006.12673: pdf, ps.