On planar algebraic curves and holonomic D-modules in positive characteristic

Alexei Belov-Kanel, Andrey Elishev

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In this paper we study a correspondence between cyclic modules over the first Weyl algebra and planar algebraic curves in positive characteristic. In particular, we show that any such curve has a preimage under a morphism of certain ind-schemes. This property might pave the way to an indirect proof of existence of a canonical isomorphism between the group of algebra automorphisms of the first Weyl algebra over the field complex numbers and the group of polynomial symplectomorphisms of ℂ2.

Original languageEnglish
Article number1650155
JournalJournal of Algebra and its Applications
Issue number8
StatePublished - 1 Oct 2016

Bibliographical note

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© 2016 World Scientific Publishing Company.


  • Automorphisms of Weyl algebra
  • Belov-Kanel-Kontsevich conjecture
  • holonomic D-modules
  • polynomial symplectomorphisms


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