A finiteness result for post-critically finite polynomials
Number Theory
2011-02-15 v2 Dynamical Systems
Abstract
We show that the set of complex points in the moduli space of polynomials of degree d corresponding to post-critically finite polynomials is a set of algebraic points of bounded height. It follows that for any B, the set of conjugacy classes of post-critically finite polynomials of degree d with coefficients of algebraic degree at most B is a finite and effectively computable set. In the case d=3 and B=1 we perform this computation. The proof of the main result comes down to finding a relation between the "naive" height on the moduli space, and Silverman's critical height.
Cite
@article{arxiv.1010.3393,
title = {A finiteness result for post-critically finite polynomials},
author = {Patrick Ingram},
journal= {arXiv preprint arXiv:1010.3393},
year = {2011}
}
Comments
Version 2: several errors have been corrected, and some new material added. The inequalities in the main result have changed slightly