Strong approximation for the total space of certain quadric fibrations

Abstract

Let X be a variety over a number field F . For simplicity, let us assume in this introduction that the set X(F ) of rational points is not empty. Let S be a finite set of places of F . One says that strong approximation holds for X off S if the diagonal image of the set X(F ) of rational points is dense in the space of S-adeles X(AF ) (these are the adeles where the places in S have been omitted) equipped with the adelic topology. If this property holds for X , it in particular implies a local-global principle for the existence of integral points on integral models of X over the ring of S-integers of F . For X projective, X(AF ) = ∏