Kontsevich's holonomic-module and Lagrangian-subvariety conjecture

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Let WnW_n be the nn-th Weyl algebra, let irreducible holonomic D\mathcal D-modules mean irreducible holonomic modules over WnW_n, 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 D\mathcal D-modules over WnW_n and Lagrangian subvarieties of the affine space of corresponding dimension.

This conjecture connects holonomic D\mathcal D-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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