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

Lian Duan, Xiyuan Wang, Ariel Weiss

Let $(\ddot{I}{}_{\hat{I}}»:G_{\mathbb{Q}}\to {\mathrm{GL}}_5({\overline{E}}_{\hat{I}}»){)}_{\hat{I}}»$ be a strictly compatible system of Galois representations such that no Hodge--Tate weight has multiplic…