Irréductibilité de la première équation de Painlevé

Abstract: A definition of reducibility for algebraic codimension two foliations given by closed 2-forms is proposed. Reducible foliations are characterised on theirs Galois groupoids. We apply this to the foliation given by the first Painlevé equation. Its Galois groupoid is computed and this proves its irreducibility. To cite this article: G. Casale, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]