2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139672Let $G$ be the linear algebraic group $SL_3$ over a field $k$ of characteristic two. Let $A$ be a finitely generated commutative $k$-algebra on which $G$ acts rationally by $k$-algebra automorphisms. We show that the full cohomology ring $H^*(G,A)$ is finitely generated. This extends the finite generation property of the ring of invariants $A^G$. We discuss where the problem stands for other geometrically reductive group schemes.16 pages; minor changes; final versionRepresentation Theory20G10; 14L24text