Effective Height Upper Bounds on Algebraic Tori
Abstract
The main emphasis will be on height upper bounds in the algebraic torus Gnm. 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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