Z. Reichstein, B. Youssin, On a property of special groups , Transformation Groups, 6, no. 3 (2001), 261-266.

Abstract: Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We show that if H^1(K, G) = { 1 } for some finitely generated field extension K_0/k of transcendence degree > 2 then H^1(L, G) = { 1 } for every field extension L/k. This shows that Serre's conjectures I and II have no analogues for fields of cohomological dimentsion > 2.

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