English

Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring

Commutative Algebra 2012-04-20 v9 Algebraic Geometry

Abstract

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger results are obtained. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if A is a Q-algebra. Another crucial ingredient, of interest in itself, is that stable tameness is a local property: If an automorphism is locally tame, then it is stably tame.

Keywords

Cite

@article{arxiv.0707.3151,
  title  = {Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring},
  author = {Joost Berson and Arno van den Essen and David Wright},
  journal= {arXiv preprint arXiv:0707.3151},
  year   = {2012}
}

Comments

18 pages

R2 v1 2026-06-21T09:00:20.550Z