%0 Journal Article
%T Strongly residual coordinates over A[x]
%A Drew Lewis
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/978-3-319-05681-4_23
%X For a domain A of characteristic zero, a polynomial f over A[x] is called a strongly residual coordinate if f becomes a coordinate (over A) upon going modulo x, and f becomes a coordinate upon inverting x. We study the question of when a strongly residual coordinate is a coordinate, a question closely related to the Dolgachev-Weisfeiler conjecture. It is known that all strongly residual coordinates are coordinates for n=2 . We show that a large class of strongly residual coordinates that are generated by elementaries upon inverting x are in fact coordinates for arbitrary n, with a stronger result in the n=3 case. As an application, we show that all Venereau-type polynomials are 1-stable coordinates.
%U http://arxiv.org/abs/1304.1765v2