A Counter-example to the Cancellation Problem for the Affine Space A³ in characteristic p

2012/08/02 by Neena Gupta, Gupta, Neena
Mathematics · #14R10 #Advanced Differential Equations and Dynamical Systems #Advanced Harmonic Analysis Research #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1208.0483

openalex publication_date 2012/08/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that the Cancellation Conjecture does not hold for the affine space A³_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].

Related

• An Analytic Approach to The Cancellation Problem for Affine Spaces over ℂ
• An Algebraic characterization of the affine three space in arbitrary characteristic
• On Zariski's Cancellation Problem in positive characteristic
• Affine open subsets in A³ without the cancellation property
• Algebraic families of higher dimensional \mathbbA¹-contractible affine varieties non-isomorphic to affine spaces