Explicit formulas for arithmetic support of differential and difference operators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918024247771136 |
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| author | Kontsevich, Maxim Odesskii, Alexander |
| author_facet | Kontsevich, Maxim Odesskii, Alexander |
| contents | We compute arithmetic support of the formal deformations $D=P+tQ_1+t^2Q_2+...$ of the differential operator $P=(x\partial_x-r_1)...(x\partial_x-r_k)$, where $r_1,...,r_k\in\mathbb{Q}$ for sufficiently large primes $p$ in terms of the monodromy of $D$ in characteristic zero. An analog of these results is also provided in the case of $q$-difference operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit formulas for arithmetic support of differential and difference operators Kontsevich, Maxim Odesskii, Alexander Algebraic Geometry Number Theory Quantum Algebra We compute arithmetic support of the formal deformations $D=P+tQ_1+t^2Q_2+...$ of the differential operator $P=(x\partial_x-r_1)...(x\partial_x-r_k)$, where $r_1,...,r_k\in\mathbb{Q}$ for sufficiently large primes $p$ in terms of the monodromy of $D$ in characteristic zero. An analog of these results is also provided in the case of $q$-difference operators. |
| title | Explicit formulas for arithmetic support of differential and difference operators |
| topic | Algebraic Geometry Number Theory Quantum Algebra |
| url | https://arxiv.org/abs/2505.12480 |