Effective Height Upper Bounds on Algebraic Tori

Details Effective Height Upper Bounds on Algebraic Tori Effective Height Upper Bounds on Algebraic Tori

2012-01-16

arxiv.org/abs/1201.3255v1

Mathematics

Number Theory

This manuscript was written for the CIRM Workshop "La conjecture de Zilber-Pink" held in Luminy, May 2011 and organized by Ga\

Scientific paper

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.

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