Some Stably Tame Polynomial Automorphisms

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

We study the structure of length three polynomial automorphisms of $R[X,Y]$
when $R$ is a UFD. These results are used to prove that if
$\text{SL}_m(R[X_1,X_2,..., X_n]) = \text{E}_m(R[X_1,X_2,..., X_n])$ for all
$n,\ge 0$ and for all $m \ge 3$ then all length three polynomial automorphisms
of $R[X,Y]$ are stably tame.

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