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 B₁, ,Bᵣ∈ GLₘ(K) be matrices with multiplicatively independent eigenvalues and let V be a closed subvariety of GLₘ(K) not passing through zero. Then there exist only finitely many elements of GLₘ(K) of the form B₁n₁⋯ Bᵣnᵣ (as we vary n₁, ,nᵣ in Z ) lying on the subvariety V .
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Bell et al. (2024) studied this question.
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