On Planar Algebraic Curves and Holonomic $\mathcal{D}$-modules in   Positive Characteristic
  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 for 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 $\mathbb{C}^2$. 
Alexei Kanel-Belov and Andrey Elishev
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