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arXiv · 1307.3748

A Bogomolov type statement for function fields

Dragos Ghioca
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Abstract

Let k be a an algebraically closed field of arbitrary characteristic, and we let h be the usual Weil height for the n-dimensional affine space corresponding to the function field k(t) (extended to its algebraic closure). We prove that for any affine variety V defined over the algebraic closure of k(t), there exists a positive real number c such that if P is an algebraic point of V and h(P)< c, then P has its coordinates in k.

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Dragos Ghioca. 2013-07-14. A Bogomolov type statement for function fields. https://arxiv.org/abs/1307.3748

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