2024/06/13 by Benjamin Castle, Castle, Benjamin
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Logic (math.LO) #Primary 03C45 #Secondary 03C64
paper · pdf · doi:10.48550/arxiv.2406.09285
openalex publication_date 2024/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the higher dimensional case of the o-minimal variant of Zilber's Restricted Trichotomy Conjecture. More precisely, let \mathcal R be an o-minimal expansion of a real closed field, let M be an interpretable set in \mathcal R, and let \mathcal M=(M,...) be a reduct of the induced structure on M. If \mathcal M is strongly minimal and not locally modular, then dim\mathcal R(M)=2. As an application, we prove the Zilber trichotomy for all strongly minimal structures interpreted in the theory of compact complex manifolds.