Crystalline Chebotarëv density conjecture

Let $U$ be the curve, let $K$ be the specified finite totally ramified extension, and let ${\mathcal{F}}$ be a convergent $F$-isocrystal on $U$. Fix $u\in U({\mathbb{F}}_{q^e})$, and write $\operatorname{Gr}({\mathcal{F}}/U,u)$ for its monodromy group and $\operatorname{Frob}_x({\mathcal{F}})$ for the Frobenius conjugacy class attached to each closed point $x\in|U|$. Crystalline Chebotarëv density conjecture. For every subset $S\subset|U|$ of Dirichlet density one, the set

$$\bigcup_{x\in S}\operatorname{Frob}_x({\mathcal{F}})$$

is Zariski-dense in $\operatorname{Gr}({\mathcal{F}}/U,u)$. This is the crystalline analogue of Chebotarëv's density theorem. The source also notes that the Zariski topology is the expected appropriate topology; the conjecture's resolution is not specified here.