Serre's Sato–Tate equidistribution conjecture for generic abelian varieties

Let $A$ be a generic abelian $g$-fold over $\mathbb{Q}$, meaning that the image of its adelic Galois representation is open in $\operatorname{GSp}_{2g}(\hat{\mathbb{Z}})$. Let $a_p(A)$ denote the Frobenius trace at a prime $p$ of good reduction, and let $\Phi_{\operatorname{USp}(2g)}$ be the trace distribution induced by Haar measure on $\operatorname{USp}(2g)$. Serre's Sato–Tate conjecture. The normalized traces $\frac{a_p(A)}{\sqrt p}$ are equidistributed in $[-2g,2g]$ with respect to $\Phi_{\operatorname{USp}(2g)}$. This is a main form of the Sato–Tate conjecture; it is known for elliptic curves over $\mathbb{Q}$, but is not known in general for $g\geq 2$.