The profinite polynomial automorphism group
Algebraic Geometry
2015-07-13 v1 Commutative Algebra
Abstract
We introduce an extension of the (tame) polynomial automorphism group over finite fields: the profinite (tame) polynomial automorphism group, which is obtained by putting a natural topology on the automorphism group. We show that most known candidate non-tame automorphisms are inside the profinite tame polynomial automorphism group, giving another result showing that tame maps are potentially "dense" inside the set of automorphisms. We study the profinite tame automorphism group and show that it is not far from the set of bijections obtained by endomorphisms.
Cite
@article{arxiv.1410.8334,
title = {The profinite polynomial automorphism group},
author = {Stefan Maubach and Abdul Rauf},
journal= {arXiv preprint arXiv:1410.8334},
year = {2015}
}
Comments
24 pages