2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79287Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We give a simple proof of the following result: if H^1(L, G) = {1} for some finitely generated field extension L/k of transcendence degree \ge 3 then H^1(K, G) = {1} for every field extension K/k.AMS LaTeX 1.1, 4 pages. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.htmlAlgebraic GeometryGroup Theorytext