On the Cancellation Problem for the Affine SpaceA 3 in characteristic p

Abstract

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[X1, X2, X3] although A[T] is isomorphic to k[X1, X2, X3, X4].