The tame automorphism group in two variables over basic Artinian rings

Details The tame automorphism group in two variables over basic Artinian rings The tame automorphism group in two variables over basic Artinian rings

2009-10-19

arxiv.org/abs/0910.3519v1

Mathematics

Commutative Algebra

10 pages

Scientific paper

In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk Theorem, which deals with the case that R is a field (of any characteristic). Here we will show that for tameness over an Artinian ring, the Q-algebra assumption is really needed: we will give, for local Artinian rings with square-zero principal maximal ideal, a complete description of the tame automorphism subgroup. This will lead to an example of a non-tame automorphism, for any characteristic p>0.

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