2022/09/01 by Castle, Benjamin
#Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2209.00730
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.