PCF All The Way Down

Abstract

We prove that a finite surjective post-critically finite self-map of a variety in characteristic zero remains post-critically finite on every preperiodic integral effective divisor after passing to its periodic image with its return map. Iterating this result proves PCF all the way down. A detailed report on AI usage is contained in the manuscript.

arXiv commentPALOMAR-2026-10-30-000004 v1