The third unramified cohomology group is shown to vanish on certain varieties equipped with a pencil of quadrics or of smooth complete intersections of two quadrics. Over the complex field, this shows that the integral Hodge conjecture in degree 4 holds for such varieties. --- On \'etablit la nullit\'e du troisi\`eme groupe de cohomologie non ramifi\'ee pour certaines vari\'et\'es munies d'un pinceau de quadriques ou d'intersections compl\`etes lisses de deux quadriques. Sur les complexes, ceci permet d'\'etablir la conjecture de Hodge enti\`ere en degr\'e 4 pour de telles vari\'et\'es.
Categories: math.AG math.KT
