Explicit formulas for arithmetic support of differential and difference operators

We compute arithmetic support of the formal deformations $D=P+t{Q}_1+t^2{Q}_2+\mathrm{.}\mathrm{.}\mathrm{.}$ of the differential operator $P=(x{\mathrm{\partial }}_x-r_1)\mathrm{.}\mathrm{.}\mathrm{.}(x{\mathrm{\partial }}_x-r_k)$, where $r_1,\mathrm{.}\mathrm{.}\mathrm{.},r_k\in \mathbb{Q}$ 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.