Restricted Trichotomy in Characteristic Zero
Logic
2022-09-05 v1 Algebraic Geometry
Abstract
We prove the characteristic zero case of Zilber's Restricted Trichotomy Conjecture. That is, we show that if is any non-locally modular strongly minimal structure interpreted in an algebraically closed field of characteristic zero, then itself interprets ; in particular, any non-1-based structure interpreted in is mutually interpretable with . 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.
Keywords
Cite
@article{arxiv.2209.00730,
title = {Restricted Trichotomy in Characteristic Zero},
author = {Benjamin Castle},
journal= {arXiv preprint arXiv:2209.00730},
year = {2022}
}
Comments
75 pages