On weak approximation in algebraic groups and related varieties defined by systems of forms
The main objects of the reviewed paper are semisimple linear algebraic groups \(G\) of the adjoint type defined over an arbitrary field \(k\). The author is interested whether the weak approximation property with respect to an arbitrary finite set of valuations holds for \(G\). It turns out that the answer is positive for many classical and exceptional groups as well as for some related varieties defined by a system of forms. For groups defined over a global field \(k\), the author considers another approximation property (integral approximation) which is in a sense intermediate between weak and strong approximation. He proves (under mild restrictions on a connected \(k\)-group \(G\)) that this property holds outside some finite set of valuations of \(k\). Some of these results were announced in an earlier paper [the author, Contemp. Math. 131, Pt. 1, 423-426 (1992; Zbl 0763.11021)].
scientific article; zbMATH DE number 943212
scientific article