The Sato--Tate conjecture for abelian varieties

Let $A$ be an abelian variety over a number field $K$, and let $\operatorname{ST}(A)$ be its Sato--Tate group. For each prime $\mathfrak{p}$ of good reduction, let $x_{\mathfrak{p}}$ be the conjugacy class in $\operatorname{ST}(A)$ of the normalized Frobenius image, with the primes ordered by norm. Let $X$ be the space of conjugacy classes of $\operatorname{ST}(A)$, and let $\mu$ be the pushforward of Haar measure to $X$. Sato--Tate conjecture. The sequence $(x_{\mathfrak{p}})$ is equidistributed with respect to $\mu$.

This conjecture predicts the distribution of normalized Frobenius conjugacy classes for abelian varieties. The source states the conjecture in general and notes that the relevant independence of the auxiliary choices is known for dimensions at most three but remains open in general.