Submission date: 1 September 2022

Abstract:

We prove the characteristic zero case of Zilber's Restricted Trichotomy Conjecture. That is, we show that if M is any non-locally modular strongly minimal structure interpreted in an algebraically closed field K of characteristic zero, then M itself interprets K; in particular, any non-1-based structure interpreted in K is mutually interpretable with K. Notably, we treat both the `one-dimensional' and `higher-dimensional' cases of the conjecture, introducing new tools to resolve the higher-dimensional case and then using the same tools to recover the previously known one-dimensional case.

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Full text arXiv 2209.00730: pdf, ps.