A MORDELL-LANG-TYPE PROBLEM FOR GLm

We prove a nonabelian variant of the classical Mordell-Lang conjecture in the context of finite- dimensional central simple algebras. We obtain the following result as a particular case of a more general statement. Let K be an algebraically closed field of characteristic zero, let B (1) , ... , B-r is an element of GL(m)(K) be matrices with multiplicatively independent eigenvalues and let V be a closed subvariety of GL(m)(K) not passing through zero. Then there exist only finitely many elements of GL(m)(K) of the form B-1(n1) <middle dot> <middle dot> <middle dot> B-r(nr) (as we vary n(1),... , ... , n(r ) in Z) lying on the subvariety V .