The Chebotarev-Sato-Tate equidistribution conjecture for abelian varieties

Let $A$ be an abelian variety over a number field $F$, let $K/F$ be the extension appearing in the definition of the Chebotarev-Sato-Tate group, and let $ST_A\subset \mathrm{USp}(2g)$ be the Sato-Tate group of $A$. Set $ST=ST_A\times \mathrm{Gal}(K/F)$, let $X$ be the set of conjugacy classes of $ST$, and let $\mu$ be the product of Haar measure on $ST_A$ and the discrete measure on $\mathrm{Gal}(K/F)$. For each prime $\mathfrak{p}\notin S$, let $x_{\mathfrak{p}}$ be the conjugacy class of $g_{\mathfrak{p}}q_{\mathfrak{p}}^{-1/2}\times\sigma_{\mathfrak{p}}$ in $ST$, where $g_{\mathfrak{p}}$ is the normalized Frobenius element and $\sigma_{\mathfrak{p}}$ is the Artin symbol of $\mathfrak{p}$ in $\mathrm{Gal}(K/F)$. Chebotarev-Sato-Tate conjecture. The sequence $\{x_{\mathfrak{p}}\}_{\mathfrak{p}\notin S}$, with the primes $\mathfrak{p}$ ordered by norm, is equidistributed on $X$ with respect to the pushforward of the Haar measure $\mu$ on $ST$ to $X$. This is the central hybrid Chebotarev-Sato-Tate assertion of the paper; the supplied material does not state whether it has been proved in full generality or remains open.