Mod-5 Galois images from abelian surfaces

Aidan Hennessey, Mathilde Kermorgant, Andy Zhu

For $J$ an abelian surface, the Galois representation $\varrho_{J, \ell} : {\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \rightarrow {\rm Aut}(J[\ell]) \simeq {\rm GSp}_4(\mathbb{F}_…