On the cancellation problem for the affine space A~3 in characteristic p

摘要

We show that the Cancellation Conjecture does not hold for the affine space A_k~3 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].