PCF All The Way Down — Draconitic Research

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.

Cite

BibTeX RIS

BibTeX

@misc{dupuy2026down,
  title = {{PCF All The Way Down}},
  author = {Taylor Dupuy and Alon Levy and Thomas Tucker and Zhouran Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06106},
  eprint = {2611.06106},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06106},
  note = {CC BY-SA 4.0},
}

RIS

TY  - UNPB
TI  - PCF All The Way Down
AU  - Taylor Dupuy
AU  - Alon Levy
AU  - Thomas Tucker
AU  - Zhouran Wang
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06106
UR  - https://arxiv.org/abs/2611.06106
AB  - 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.
ER  -