Vp. Platonov et Vi. Chernousov, THE RATIONALITY PROBLEM FOR GROUP VARIETIES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 322(3), 1996, pp. 245-250
Let K be a finite extension of the p-adic field Q(p), and let G be a s
imple algebraic group defined over K. We prove that the variety G is K
-rational, provided G is not of type A(n), n > 2.