In this paper it is established 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 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 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.
Berson, Joost; van den Essen, Arno; and Wright, David, "Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring" (2012). Mathematics Faculty Publications. 5.