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arXiv · 0707.3151

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

Joost Berson·Arno van den Essen·David Wright
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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.

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Joost Berson, Arno van den Essen, David Wright. 2012-04-19. Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring. https://arxiv.org/abs/0707.3151

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