  We give a new axiomatic treatment of the Zilber trichotomy, and use it to
complete the proof of the trichotomy for relics of algebraically closed fields,
i.e., reducts of the ACF-induced structure on ACF-definable sets. More
precisely, we introduce a class of geometric structures equipped with a
Hausdorff topology, called \textit{Hausdorff geometric structures}. Natural
examples include the complex field; algebraically closed valued fields;
o-minimal expansions of real closed fields; and characteristic zero Henselian
fields (in particular $p$-adically closed fields). We then study the Zilber
trichotomy for relics of Hausdorff geometric structures, showing that under
additional assumptions, every non-locally modular strongly minimal relic on a
real sort interprets a one-dimensional group. Combined with recent results,
this allows us to prove the trichotomy for strongly minimal relics on the real
sorts of algebraically closed valued fields.
  Finally, we make progress on the imaginary sorts, reducing the trichotomy for
\textit{all} ACVF relics (in all sorts) to a conjectural technical condition
that we prove in characteristic $(0,0)$.
