A New Northcott Property for Faltings Height
Number Theory
2017-09-20 v1 Algebraic Geometry
Abstract
In this work we prove a new Northcott property for the Faltings height. Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that there are finitely many CM abelian varieties over the complex numbers of a fixed dimension which have bounded Faltings height. The technique developed uses new tools from integral p-adic Hodge theory to study the variation of Faltings height within an isogeny class of CM abelian varieties. In special cases, we are moreover able to use the technique to develop new Colmez-type formulas for the Faltings height.
Keywords
Cite
@article{arxiv.1709.06098,
title = {A New Northcott Property for Faltings Height},
author = {Lucia Mocz},
journal= {arXiv preprint arXiv:1709.06098},
year = {2017}
}
Comments
62 pages, comments welcome