[Modules holonomes et 1-génération dans la conjecture jacobienne]
Let
The Jacobian Conjecture (JC) says that every Jacobian map is an automorphism. Clearly, the Jacobian Conjecture is true iff the twisted (by
A short direct algebraic (without reduction to prime characteristic) proof is given of the equivalence of the Jacobian and the Poisson Conjectures (this gives a new short proof of the equivalence of the Jacobian, Poisson and Dixmier Conjectures).
Soit
La Conjecture Jacobienne (CJ) affirme que chaque application jacobienne est un automorphisme. Clairement, la Conjecture Jacobienne est vraie si le module tordu (par
Une démonstration directe et brève (sans réduction à la caractéristique première) est donnée de l’équivalence des Conjectures Jacobienne et Poisson (ceci donne une nouvelle démonstration brève de l’équivalence des Conjectures Jacobienne, Poisson et Dixmier).
Révisé le :
Accepté le :
Publié le :
Keywords: The Jacobian Conjecture, the Conjecture of Dixmier, the Weyl algebra, the holonomic module, the endomorphism algebra, the length, the multiplicity
Mots-clés : La conjecture jacobienne, la conjecture de Dixmier, l’algèbre de Weyl, le module holonomique, l’algèbre des endomorphismes, la longueur, la multiplicité
Volodymyr V. Bavula 1

@article{CRMATH_2024__362_G7_731_0, author = {Volodymyr V. Bavula}, title = {Holonomic modules and 1-generation in the {Jacobian} {Conjecture}}, journal = {Comptes Rendus. Math\'ematique}, pages = {731--738}, publisher = {Acad\'emie des sciences, Paris}, volume = {362}, year = {2024}, doi = {10.5802/crmath.556}, language = {en}, }
Volodymyr V. Bavula. Holonomic modules and 1-generation in the Jacobian Conjecture. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 731-738. doi : 10.5802/crmath.556. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.556/
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