English

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 M\mathcal M is any non-locally modular strongly minimal structure interpreted in an algebraically closed field KK of characteristic zero, then M\mathcal M itself interprets KK; in particular, any non-1-based structure interpreted in KK is mutually interpretable with KK. 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

R2 v1 2026-06-28T00:36:03.447Z