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