3 problems

Let $A$ be an abelian variety of ${\mathrm{GL}}_2$-type over ${\mathbb Q}$, meaning that its rational endomorphism algebra contains a number field of degree equal to ${\rm dim} A$.…

Let $g$ be even and let $\mathsf{A}^{(g)}_a$ be the Jacobian in the family described above, with $a$ ranging over the parameter space. The geometric endomorphism ring is expected t…

Let $B$ range over QM abelian fourfolds over $\mathbb{Q}$ of conductor $N^2$, and let $f$ range over cuspidal, nonlift Siegel paramodular newforms of genus $2$, weight $2$, and lev…