Restricted Trichotomy Conjecture in concrete form

Let $K$ be an algebraically closed field, and let $\mathcal M=(M,...)$ be a non-locally modular strongly minimal structure. Assume that the universe $M$ of $\mathcal M$, as well as all $\mathcal M$-definable subsets of cartesian powers of $M$, are constructible sets over $K$, meaning finite Boolean combinations of affine algebraic sets. Restricted Trichotomy Conjecture. Then $\mathcal M$ interprets an infinite field.

This is a concrete reformulation of the restricted trichotomy conjecture for structures whose underlying sets and definable sets are constructible over an algebraically closed field. The paper states that the conjecture is proved when $K=\mathbb C$, and that the general characteristic-zero case follows from this result and basic model theory.