To be or not to be local

Christophe Breuil, Florian Herzig, Yongquan Hu +4

Let $p$ be a prime number and $K$ a finite unramified extension of ${\mathbf{Q}}_p$. For a smooth representation $\pi$ of ${\mathrm{GL}}_2(K)$ occurring in some Hecke eigenspace of the m…