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Proof of Two-dimensional Jacobian Conjecture
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Version 1
: Received: 8 December 2022 / Approved: 9 December 2022 / Online: 9 December 2022 (07:12:06 CET)
Version 2 : Received: 1 September 2023 / Approved: 4 September 2023 / Online: 6 September 2023 (03:33:44 CEST)
Version 2 : Received: 1 September 2023 / Approved: 4 September 2023 / Online: 6 September 2023 (03:33:44 CEST)
How to cite: Su, Y. Proof of Two-dimensional Jacobian Conjecture. Preprints 2022, 2022120171. https://doi.org/10.20944/preprints202212.0171.v2 Su, Y. Proof of Two-dimensional Jacobian Conjecture. Preprints 2022, 2022120171. https://doi.org/10.20944/preprints202212.0171.v2
Abstract
Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.
Keywords
Jacobian conjecture; Keller maps; injectivity of Keller maps
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (1)
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Commenter: Su Yucai
Commenter's Conflict of Interests: Author
is a very kind and warmhearted professor, willing to spend more than six months of all his day-and-night's valuable time, selflessly, seriously, and meticulously helping me thoroughly examine every detail of the paper, discussing with me and giving a huge number of useful comments, suggestions and providing simple proofs of Theorem 1.3 and Proposition 3.8. Before that, we do not personally know each other. I have great respect for him and admire his incomparably broad knowledge, mind and thoughts. Anybody who compares the present version with any version before December 2022 can see how much hard work has been done by him. Without his help, the paper cannot be the present form.