Effective Height Upper Bounds on Algebraic Tori
Number Theory
2012-01-17 v1
Abstract
The main emphasis will be on height upper bounds in the algebraic torus G^{n}_{m}. By height we will mean the absolute logarithmic Weil height. Section 3.2 contains a precise definition of this and other more general height functions. The first appendix gives a short overview of known results in the abelian case. The second appendix contains a few height bounds in Shimura varieties.
Keywords
Cite
@article{arxiv.1201.3255,
title = {Effective Height Upper Bounds on Algebraic Tori},
author = {Philipp Habegger},
journal= {arXiv preprint arXiv:1201.3255},
year = {2012}
}
Comments
This manuscript was written for the CIRM Workshop "La conjecture de Zilber-Pink" held in Luminy, May 2011 and organized by Ga\"el R\'emond and Emmanuel Ullmo