Constructing abelian varieties from rank 3 Galois representations with real trace field

Raju Krishnamoorthy, Yeuk Hay Joshua Lam

Let $U/K$ be a smooth affine curve over a number field and let $L$ be an irreducible rank 3 ${\overline{\mathbb{Q}}}_{\ell }$-local system on $U$ with trivial determinant and infinite…