Jacobian Conjecture via Differential Galois Theory
Copyright policy )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 strongly normal extensions as presented by Kovacic and the characterization of Picard-Vessiot extensions in terms of tensor products given by Levelt.
- Jagiellonian University Poland
- AGH University of Science and Technology Poland
- University of Barcelona Spain
strongly normal extensions, Mathematics - Algebraic Geometry, polynomial automorphisms, Separable extensions, Galois theory, FOS: Mathematics, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Jacobian problem, Algebraic Geometry (math.AG), Derivations and commutative rings, 14R10, 14R15, 13N15, 12F10
strongly normal extensions, Mathematics - Algebraic Geometry, polynomial automorphisms, Separable extensions, Galois theory, FOS: Mathematics, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Jacobian problem, Algebraic Geometry (math.AG), Derivations and commutative rings, 14R10, 14R15, 13N15, 12F10
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