Constructing abelian varieties from rank 2 Galois representations

Raju Krishnamoorthy, Jinbang Yang, Kang Zuo

Let $U$ be a smooth affine curve over a number field $K$ with a compactification $X$ and let $\mathbb{L}$ be a rank $2$, geometrically irreducible ${\bar{\mathbb{Q}}}_{\ell }$-local syste…