Tsuchimoto, Yoshifumi Endomorphisms of Weyl algebra and \(p\)-curvatures. (English) Zbl 1105.16024 Osaka J. Math. 42, No. 2, 435-452 (2005). 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. Reviewer: Angela Gammella (Creil) Cited in 3 ReviewsCited in 28 Documents MSC: 16S32 Rings of differential operators (associative algebraic aspects) 14R15 Jacobian problem 16W20 Automorphisms and endomorphisms 17B63 Poisson algebras Keywords:Weyl algebras; symplectic forms; connections; endomorphisms; Dixmier conjecture; Jacobian conjecture PDFBibTeX XMLCite \textit{Y. Tsuchimoto}, Osaka J. Math. 42, No. 2, 435--452 (2005; Zbl 1105.16024)