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En l'honneur de H. Hironaka pour son 80ème anniversaire.International audienceAfter a short review on foliations, we prove that a codimension 1 holomorphic foliation on $\mathbb P^3_{\mathbb C}$ with simple singularities is given by a closed rational 1-form. The proof uses Hironaka-Matsumura prolongation theorem of formal objects

Codimension one holomorphic foliations on $${\mathbb P^n_{\mathbb C}}$$ : problems in complex geometry