Abstract
We show that the Cancellation Conjecture does not hold for the affine space \(\mathbb{A}^{3}_{k}\) 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].
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The author thanks Professors Shrikant M. Bhatwadekar, Amartya K. Dutta and Nobuharu Onoda for carefully going through the earlier draft and suggesting improvements.
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Gupta, N. On the cancellation problem for the affine space \(\mathbb{A}^{3}\) in characteristic p . Invent. math. 195, 279–288 (2014). https://doi.org/10.1007/s00222-013-0455-2
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DOI: https://doi.org/10.1007/s00222-013-0455-2