English

A Counter-example to the Cancellation Problem for the Affine Space A^3 in characteristic p

Commutative Algebra 2013-01-24 v2 Algebraic Geometry

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[X_1,X_2,X_3] although A[T] is isomorphic to k[X_1, X_2, X_3, X_4].

Keywords

Cite

@article{arxiv.1208.0483,
  title  = {A Counter-example to the Cancellation Problem for the Affine Space A^3 in characteristic p},
  author = {Neena Gupta},
  journal= {arXiv preprint arXiv:1208.0483},
  year   = {2013}
}

Comments

Final version. To appear in Invent. Math