Heights and arithmetic dynamics over finitely generated fields
Number Theory
2020-10-15 v1
Abstract
We develop a theory of vector-valued heights and intersections defined relative to finitely generated extensions K/k. These generalize both number field and geometric heights. When k is Q or F_p, or when a non-isotriviality condition holds, we obtain Northcott-type results. We then prove a version of the Hodge Index Theorem for vector-valued intersections, and use it to prove a rigidity theorem for polarized dynamical systems over any field.
Keywords
Cite
@article{arxiv.2010.07200,
title = {Heights and arithmetic dynamics over finitely generated fields},
author = {Alexander Carney},
journal= {arXiv preprint arXiv:2010.07200},
year = {2020}
}