On a property of special groups

Zinovy Reichstein, Boris Youssin

Published 1999-10-26Version 1

Let 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.