Strongly minimal reducts of algebraically closed valued fields (2023)
In this thesis we prove the following restricted version of Zilber's Trichotomy: Let $K=(K,+,·,v,Γ)$ be an algebraically closed valued field and let $(G,\+)$ be a K$-definable group that is either the multiplicative group or contains a finite index subgroup that is $ K$-definably isomorphic to a $K$-definable subgroup of $(K,+)$. Then if $\mathcal G=(G,\+,…)$ is a strongly minimal non locally modular structure definable in $ K$ and expanding $(G,\oplus)$, it interprets an infinite field.