Article 2187 (5 more) in sci.math.research (moderated):
From: David Rusin <rusin@mp.cs.niu.edu>
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]