A characterization of Keller maps
Commutative Algebra
2013-06-21 v2 Algebraic Geometry
Abstract
Let k be a field of characteristic zero. Let phi be a k-endomorphism of the polynomial algebra k[x_1,...,x_n]. It is known that phi is an automorphism if and only if it maps irreducible polynomials to irreducible polynomials. In this paper we show that phi satisfies the jacobian condition if and only if it maps irreducible polynomials to square-free polynomials. Therefore, the Jacobian Conjecture is equivalent to the following statement: every k-endomorphism of k[x_1,...,x_n], mapping irreducible polynomials to square-free polynomials, maps irreducible polynomials to irreducible polynomials.
Cite
@article{arxiv.1109.2113,
title = {A characterization of Keller maps},
author = {Piotr Jedrzejewicz},
journal= {arXiv preprint arXiv:1109.2113},
year = {2013}
}
Comments
Lemma 3.5 has been corrected