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arXiv · 2106.09912

Quantization of restricted Lagrangian subvarieties in positive characteristic

Joshua Mundinger
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Abstract

Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X in positive characteristic which endow the Poisson bracket on X with the structure of a restricted Lie algebra. We consider deformation quantization of line bundles on Lagrangian subvarieties Y of X to modules over such quantizations. If the ideal sheaf of Y is a restricted Lie subalgebra of the structure sheaf of X, we show that there is a certain cohomology class which vanishes if and only if a line bundle on Y admits a quantization.

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Joshua Mundinger. 2021-06-18. Quantization of restricted Lagrangian subvarieties in positive characteristic. https://doi.org/10.1016/j.aim.2022.108760

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