A Bogomolov type statement for function fields
Number Theory
2013-07-16 v1
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.
Keywords
Cite
@article{arxiv.1307.3748,
title = {A Bogomolov type statement for function fields},
author = {Dragos Ghioca},
journal= {arXiv preprint arXiv:1307.3748},
year = {2013}
}