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Endomorphisms of Weyl algebra and \(p\)-curvatures. (English) Zbl 1105.16024

This paper studies endomorphisms of Weyl algebras from an arithmetic point of view. The author first works over a positive characteristic field, then he shows how an affine space with a flat connection can be constructed for any Weyl algebra. He then defines a symplectic form in a functorial way and by taking the limit, he goes back to characteristic zero. As a byproduct, he gives an affirmative answer to the Dixmier conjecture.

MSC:

16S32 Rings of differential operators (associative algebraic aspects)
14R15 Jacobian problem
16W20 Automorphisms and endomorphisms
17B63 Poisson algebras
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