Jacobian Conjecture via Differential Galois Theory

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• Main Authors: Adamus, E., Crespo, T., Hajto, Z.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210188
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Jacobian Conjecture via Differential Galois Theory / E. Adamus, T. Crespo, Z. Hajto // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ.

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 strongl...