  We show that the Cancellation Conjecture does not hold for the affine space
A^3_k over any field k of positive characteristic. We prove that an example of
T. Asanuma provides a three-dimensional k-algebra A for which A is not
isomorphic to k[X_1,X_2,X_3] although A[T] is isomorphic to k[X_1, X_2, X_3,
X_4].
