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

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 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 SpecR. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-...

Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Dedekind Domain

In this paper it is established that all two-dimensional polynomial automorphisms over a Dedekind Q-algebra are stably tame; in fact, they become tame with the addition of three more dimensions. A key element in the proof is this additional new theorem: Over an Artinian Q-algebra all two-dimensional polynomial automorphisms having Jacobian determinant one are tame.

Two-dimensional projectively-tameness over Noetherian domains of dimension one

In this paper all coordinates in two variables over a Noetherian Q-domain of Krull dimension one are proved to be projectively tame. In order to do this, some results concerning projectively-tameness of polynomials in general are shown. Furthermore, we deduce that all automorphisms in two variables over a Noetherian reduced ring of dimension zero are tame.

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

The two-dimensional Laplace operator and tameness

We investigate the Dirichlet solution for a semianalytic continuous function on the boundary of a semianalytic bounded domain in the plane. We show that the germ of the Dirichlet solution at a boundary point with angle greater than 0 lies in a certain quasianalytic class used by Ilyashenko in his work on Hilbert’s 16 problem. With this result we can prove that the Dirichlet solution is definabl...