Peterzil's Zilber trichotomy conjecture for strongly minimal relics of o-minimal structures

Let ${\mathcal R}$ be an o-minimal structure. A strongly minimal relic of ${\mathcal R}$ is a structure whose definable sets are interpretable in ${\mathcal R}$ and which is strongly minimal.

Peterzil's conjecture. Every strongly minimal ${\mathcal R}$-relic is either locally modular or interprets an algebraically closed field.

This is the Zilber trichotomy for strongly minimal relics of o-minimal structures. The surrounding work establishes important special cases, including local modularity for relics on universes of dimension greater than $2$, but the full statement is presented here as an older conjecture of Peterzil.