On weak approximation in algebraic groups and related varieties defined by systems of forms Original Research Article

It is well-known that weak approximation holds for a large class of semisimple groups over global fields, including those which are simply connected or adjoint. Earlier Kneser suggested the investigation of weak approximation in algebraic groups over any field of definition and Platonov gave examples of simply connected groups of type 1A which do not have this property. Thus conjecturally adjoint groups satisfy weak approximation over arbitrary fields of definition. Here we prove the validity of weak approximation for many adjoint semisimple groups over arbitrary fields of definition and also for varieties, defined by a system of forms, which are closely related to adjoint groups.