Title: A characterization of uniruled Kähler manifolds.Abstract: We adapt Bost's algebraicity characterization to the situation of a germ in a compact Kähler manifold. As a consequence, we extend the algebraic integrability criteria of Campana-Paun and of Druel to foliations on compact Kähler manifolds. As an application, we prove that a compact Kähler manifold is uniruled if and […]