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arXiv · 1901.01566

Jacobian Conjecture via Differential Galois Theory

Elzbieta Adamus·Teresa Crespo·Zbigniew Hajto
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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.

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Elzbieta Adamus, Teresa Crespo, Zbigniew Hajto. 2019-01-06. Jacobian Conjecture via Differential Galois Theory. https://doi.org/10.3842/sigma.2019.034

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