Resumen de Sato-Tate distribution for abelian varieties with real multiplication over function fields

Chung Pang Mok

• We calculate the monodromy groups of some universal families of abelian varieties with real multiplication by $\mathbf{Q}(\cos\frac{2\pi}{r})$, over certain Hilbert type modular varieties over finite fields. Using Deligne's equidistribution theorem, we obtain the Sato-Tate law for the distribution of Frobenius eigenvalues of these universal families of abelian varieties.