On Planar Algebraic Curves and Holonomic $\mathcal{D}$-modules in Positive Characteristic

摘要

In this paper we study a correspondence between cyclic modules over the firstWeyl algebra and planar algebraic curves in positive characteristic. Inparticular, we show that any such curve has a preimage under a morphism ofcertain ind-schemes. This property might pave the way for an indirect proof ofexistence of a canonical isomorphism between the group of algebra automorphismsof the first Weyl algebra over the field complex numbers and the group ofpolynomial symplectomorphisms of $\mathbb{C}^2$.