2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63279We study Poisson structures over singular varieties. In this purpose, we consider the Koszul complex associated to the equations of a complete intersection. This complex forms a differential graded algebra which is equivalent to the algebra of the variety. We show that a Poisson structure is equivalent to a sequence of multiderivations over the Koszul complex. If our variety has isolated singularities, then we can construct a sequence of multiderivations of reduced form.Projet de note aux C.R.Acad.Sci.ParisRings and AlgebrasCommutative AlgebraSymplectic Geometry17B63; 53D17; 14M10; 14B05; 13N05text