On Lagrangianity of $p$-supports of holonomic D-modules and $q$-D-modules
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912928801751040 |
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| author | Etingof, Pavel |
| author_facet | Etingof, Pavel |
| contents | M. Kontsevich conjectured and T. Bitoun proved that if M is a nonzero holonomic D-module then the p-support of a generic reduction of M to characteristic p>0 is Lagrangian. We provide a new elementary proof of this theorem and also generalize it to q-D-modules. The proofs are based on Bernstein's theorem that any holonomic D-module can be transformed by an element of the symplectic group into a vector bundle with a flat connection, and a q-analog of this theorem. We also discuss potential applications to quantizations of symplectic singularities and to quantum cluster algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Lagrangianity of $p$-supports of holonomic D-modules and $q$-D-modules Etingof, Pavel Algebraic Geometry Quantum Algebra Representation Theory M. Kontsevich conjectured and T. Bitoun proved that if M is a nonzero holonomic D-module then the p-support of a generic reduction of M to characteristic p>0 is Lagrangian. We provide a new elementary proof of this theorem and also generalize it to q-D-modules. The proofs are based on Bernstein's theorem that any holonomic D-module can be transformed by an element of the symplectic group into a vector bundle with a flat connection, and a q-analog of this theorem. We also discuss potential applications to quantizations of symplectic singularities and to quantum cluster algebras. |
| title | On Lagrangianity of $p$-supports of holonomic D-modules and $q$-D-modules |
| topic | Algebraic Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2504.19329 |