# 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} }

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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