## Stable tameness of two-dimensional polynomial automorphisms over a regular ring.(English)Zbl 1246.14075

From the abstract: We establish that all two-dimensional polynomial automorphisms over a regular ring $$R$$ are stably tame. This results from the main theorem of this paper, which asserts that an automorphism in any dimension $$n$$ is stably tame if said condition holds point-wise over $$\mathrm{spec}(R)$$.
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 $$\mathbb Q$$-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.

### MSC:

 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 13F30 Valuation rings

### Keywords:

polynomial automorphisms; stable tameness
Full Text:

### References:

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