For a Shimura variety $(G, X)$ in the superrigid regime and neat level subgroup $K_{0}$ , we show that the canonical family of $\ell $ -adic representations associated to a number field point $y \in \mathrm{Sh}_{K_{0}}(G, X)(F)$ , \( \left \{ \rho _{y, \ell } \colon \mathrm{Gal}(\overline{\mathbb{Q}}/F) \to G^{\mathrm{ad}}(\mathbb{Q}_{\ell }) \right \} _{\ell }, \) form a compatible system of $G^{\mathrm{ad}}(\mathbb{Q}_{\ell })$ -representations: there is an integer $N(y)$ such that for all $\ell $ , $\rho _{y, \ell }$ is unramified away from $N(y) \ell $ , and for all $\ell \neq \ell '$ and $v \nmid N(y)\ell \ell '$ , the semisimple parts of the conjugacy classes of $\rho _{y, \ell }(\mathrm{Frob}_{v})$ and $\rho _{y, \ell '}(\mathrm{Frob}_{v})$ are (ℚ-rational and) equal. We deduce this from a stronger compatibility result for the canonical $G(\mathbb{Q}_{\ell })$ -valued local systems on connected Shimura varieties inside $\mathrm{Sh}_{K_{0}}(G, X)$ . Our theorems apply in particular to Shimura varieties of non-abelian type and represent the first such independence-of- $\ell $ results in non-abelian type.
