Deligne's conjecture on Frobenius traces for moduli of connections

Let $C_0$ be a smooth projective curve over the finite field $\mathbb F_q$ of characteristic $p>0$, let $C$ be its base change to $\overline{\mathbb F}_q$, and let $M_K$ and $M_{\overline K}$ be the moduli spaces of rank-$r$ vector bundles with integrable connection on smooth curves $C_K$ and $C_{\overline K}$, respectively. Let $E_r$ be the set of isomorphism classes of irreducible lisse $\ell'$-adic sheaves of rank $r$ on $C$, with $\ell'\neq p$. For an endomorphism $V^*$ of the $\ell'$-adic cohomology of $M_{\overline K}$, write $N_n$ for the number of its fixed points on $E_r$. Deligne's conjecture. The cohomology of $M_{\overline K}$ admits an endomorphism $V^*$ such that, for every $n\geq 1$,

$$N_n=\sum_i(-1)^i\operatorname{Tr}(V^{*n},\operatorname{H}^i(M_{\overline K})).$$

This conjecture predicts a Lefschetz-type trace formula relating the Frobenius action on the moduli of connections to fixed irreducible lisse sheaves; the source presents it as Deligne's conjecture, and no resolution is supplied here.