Diophantine Approximation on varieties III: Approximation of non-algebraic points by algebraic points

2007/11/23 by Heinrich Massold, Massold, Heinrich
Computer Science · Mathematics · #11G35 #11G50 #11J13 #11J81 #11J83 #11J85 #14G17 #14G25 #14G40 #14J20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.0711.3645

openalex publication_date 2007/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For θ a non-algebraic point on a quasi projective variety over a number field, I prove that θ has an approximation by a series of algebraic points of bounded height and degree which is essentially best possible. Applications of this result will include a proof of a slightly strengthened version of the Philippon criterion, some new algebraic independence criteria, statements concerning metric transcendence theory on varieties of arbitrary dimension, and a rather accurate estimate for the number of algebraic points of bounded height and degree on quasi projective varieties over number fields.

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