Article 2187 (5 more) in sci.math.research (moderated): From: David Rusin Subject: Are stably rational varieties rational? Date: Thu, 7 Apr 1994 09:56:23 -0500 Suppose V is an affine variety (over the rationals, say), and V x Affine space is birationally equivalent to affive space. Is the same true of V itself? Does it help to know that V is unirational (= has a rational parameterisation)? A similar question: if V x V is rational, is V? Thanks from a novice. dave rusin@math.niu.edu ============================================================================== Date: Thu, 7 Apr 94 14:06:44 -0500 From: [Permission pending] To: rusin@math.niu.edu Subject: re:Are stably rational varieties rational? No. Counterexamples were provided a few years ago by Colliot-Thelene, Sansuc and Swinnerton-Dyer. I don't have the reference handy, sorry. It was the subject of a seminar Bourbaki as well. [sig deleted -- djr]