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

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

2007-11-23

arxiv.org/abs/0711.3645v1

Mathematics

Number Theory

42 pages

Scientific paper

For $\theta$ a non-algebraic point on a quasi projective variety over a number field, I prove that $\theta$ 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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