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

Alexei Kanel-Belov; Andrey Elishev

doi:10.1142/s0219498816501553

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arXiv · 1412.6836

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

Alexei Kanel-Belov·Andrey Elishev

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Abstract

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 $\mathbb{C}^2$.

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Alexei Kanel-Belov, Andrey Elishev. 2014-12-21. On Planar Algebraic Curves and Holonomic $\mathcal{D}$-modules in Positive Characteristic. https://doi.org/10.1142/s0219498816501553

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