Analytic Curves in Algebraic Varieties over Number Fields

  title={Analytic Curves in Algebraic Varieties over Number Fields},
  author={Jean-Beno{\^i}t Bost and Antoine Chambert-Loir},
  journal={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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