Jacobian Conjecture via Differential Galois Theory
Algebraic Geometry
2019-05-06 v3
Abstract
We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partial differential fields, the theory of strongly normal extensions as presented by Kovacic and the characterization of Picard-Vessiot extensions in terms of tensor products given by Levelt.
Keywords
Cite
@article{arxiv.1901.01566,
title = {Jacobian Conjecture via Differential Galois Theory},
author = {Elzbieta Adamus and Teresa Crespo and Zbigniew Hajto},
journal= {arXiv preprint arXiv:1901.01566},
year = {2019}
}