# Analytic Curves in Algebraic Varieties over Number Fields

@article{Bost2009AnalyticCI,
title={Analytic Curves in Algebraic Varieties over Number Fields},
author={Jean-Beno{\^i}t Bost and Antoine Chambert-Loir},
journal={arXiv: Number Theory},
year={2009},
pages={69-124}
}
• Published 20 February 2007
• Mathematics
• arXiv: Number Theory
We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions on algebraic curves that extends the classical rationality theorems of Borel–Dwork and Polya–Bertrandias, valid over the projective line, to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and…
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