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arXiv · 2505.12480

Explicit formulas for arithmetic support of differential and difference operators

Maxim Kontsevich·Alexander Odesskii
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Abstract

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.

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Maxim Kontsevich, Alexander Odesskii. 2025-05-18. Explicit formulas for arithmetic support of differential and difference operators. https://arxiv.org/abs/2505.12480

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