Kontsevich's holonomic-module and Lagrangian-subvariety conjecture
Let be the -th Weyl algebra, let irreducible holonomic -modules mean irreducible holonomic modules over , and let Lagrangian subvarieties be taken in the affine space of the corresponding dimension. Kontsevich's holonomic-module conjecture. There is a one-to-one correspondence between irreducible holonomic -modules over and Lagrangian subvarieties of the affine space of corresponding dimension.
This conjecture connects holonomic -modules with their geometric characteristic data. The source states that one direction is known through work of Bitoun and Van den Bergh, that the one-dimensional case has been studied, and that results of Dodd imply a version of the conjecture; the general status is not established by the supplied information.
References
Primary source
Alexei Kanel-Belov, Andrey Elishev and Jie-Tai Yu, “Augmented Polynomial Symplectomorphisms and Quantization”, arXiv:1812.02859 (2020).
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