Nq. Thang, ON WEAK APPROXIMATION IN ALGEBRAIC-GROUPS AND RELATED VARIETIES DEFINED BY SYSTEMS OF FORMS, Journal of pure and applied algebra, 113(1), 1996, pp. 67-90
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.