ON WEAK APPROXIMATION IN ALGEBRAIC-GROUPS AND RELATED VARIETIES DEFINED BY SYSTEMS OF FORMS

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