Zilber’s restricted trichotomy in characteristic zero. (English) Zbl 07887949
Summary: We prove the characteristic zero case of Zilber’s Restricted Trichotomy Conjecture. That is, we show that if \(\mathcal{M}\) is any non-locally modular strongly minimal structure interpreted in an algebraically closed field \(K\) of characteristic zero, then \(\mathcal{M}\) 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.
MSC:
| 03C45 | Classification theory, stability, and related concepts in model theory |
| 14A99 | Foundations of algebraic geometry |
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