Algebraic leaves of algebraic foliations over number fields

@article{Bost2001AlgebraicLO,
  title={Algebraic leaves of algebraic foliations over number fields},
  author={Jean-Beno{\^i}t Bost},
  journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques},
  year={2001},
  volume={93},
  pages={161-221}
}
  • J. Bost
  • Published 1 September 2001
  • Mathematics
  • Publications Mathématiques de l'Institut des Hautes Études Scientifiques
Summary — We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field K embedded in C, a smooth algebraic variety X over K, equipped with a K-rational point P, and F an algebraic subbundle of the its tangent bundle TX, defined over K. Assume moreover that the vector bundle F is involutive, i.e., closed unter Lie bracket. Then it defines an holomorphic foliation of the analytic mainfold X(C), and one may consider its leaf… 
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