Stochastic Canonical Heights
Number Theory
2018-06-05 v2 Dynamical Systems
Abstract
We construct height functions defined stochastically on projective varieties equipped with endomorphisms, and we prove that these functions satisfy analogs of the usual properties of canonical heights. Moreover, we give a dynamical interpretation of the kernel of these stochastic height functions, and in the case of the projective line, we relate the size of this kernel to the Julia sets of the original maps. Finally, as an application, we establish the finiteness of some generalized Zsigmondy sets over global fields.
Cite
@article{arxiv.1805.10897,
title = {Stochastic Canonical Heights},
author = {Vivian Olsiewski Healey and Wade Hindes},
journal= {arXiv preprint arXiv:1805.10897},
year = {2018}
}