Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces

Lian Duan, Xiyuan Wang, Ariel Weiss

Let $({\rho }_{\lambda }:G_{\mathbb{Q}}\to {\mathrm{GL}}_5({\overline{E}}_{\lambda }){)}_{\lambda }$ be a strictly compatible system of Galois representations such that no Hodge--Tate weight has multiplicity…