Explicit formulas for arithmetic support of differential and difference operators

Maxim Kontsevich; Alexander Odesskii

paper

Explicit formulas for arithmetic support of differential and difference operators

arXiv:2505.12480

Abstract

We compute arithmetic support of the formal deformations $D = P + t Q_{1} + t^{2} Q_{2} + ...$ of the differential operator $P = (x \partial_{x} - r_{1}) ... (x \partial_{x} - r_{k})$ , where $r_{1}, ..., r_{k} \in Q$ 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.

Latex, 34 pages