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.


14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
13F30 Valuation rings
Full Text: DOI arXiv


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