Jacobian Conjecture via Differential Galois Theory
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210188 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Adamus, E. Crespo, T. Hajto, Z. 2025-12-03T14:31:16Z 2019 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. 1815-0659 2010 Mathematics Subject Classification: 14R10; 14R15; 13N15; 12F10 arXiv: 1901.01566 https://nasplib.isofts.kiev.ua/handle/123456789/210188 https://doi.org/10.3842/SIGMA.2019.034 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. This paper is dedicated to the memory of Jerald Joseph Kovacic. During his visit to Barcelona in the summer of 2008, he discussed with us algebraic aspects of the theory of strongly normal extensions. This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within the subsidy of the Ministry of Science and Higher Education. Crespo and Hajto acknowledge support by grant MTM2015-66716-P (MINECO/FEDER, UE). We thank the anonymous referees for their valuable remarks and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Jacobian Conjecture via Differential Galois Theory Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Jacobian Conjecture via Differential Galois Theory |
| spellingShingle |
Jacobian Conjecture via Differential Galois Theory Adamus, E. Crespo, T. Hajto, Z. |
| title_short |
Jacobian Conjecture via Differential Galois Theory |
| title_full |
Jacobian Conjecture via Differential Galois Theory |
| title_fullStr |
Jacobian Conjecture via Differential Galois Theory |
| title_full_unstemmed |
Jacobian Conjecture via Differential Galois Theory |
| title_sort |
jacobian conjecture via differential galois theory |
| author |
Adamus, E. Crespo, T. Hajto, Z. |
| author_facet |
Adamus, E. Crespo, T. Hajto, Z. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210188 |
| citation_txt |
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. |
| work_keys_str_mv |
AT adamuse jacobianconjectureviadifferentialgaloistheory AT crespot jacobianconjectureviadifferentialgaloistheory AT hajtoz jacobianconjectureviadifferentialgaloistheory |
| first_indexed |
2025-12-07T21:24:41Z |
| last_indexed |
2025-12-07T21:24:41Z |
| _version_ |
1850886252595773440 |