Stable tameness of two-dimensional polynomial automorphisms over a regular ring

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring RR are stably tame. This results from the main theorem of this paper, which asserts that an automorphism in any dimension nn is stably tame if said condition holds point-wise over Spec RR. A key element in the proof is a theorem which yields the following corollary: over an Artinian ring AA all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if AA is a QQ-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.