Effective Height Upper Bounds on Algebraic Tori

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.

arXiv commentThis manuscript was written for the CIRM Workshop "La conjecture de Zilber-Pink" held in Luminy, May 2011 and organized by Gaël Rémond and Emmanuel Ullmo