Companion points and locally analytic socle for ${\mathrm{GL}}_2(L)$

Yiwen Ding

Let $p>2$ be a prime number, and $L$ be a finite extension of ${\mathbb{Q}}_p$, we prove Breuil's locally analytic socle conjecture for ${\mathrm{GL}}_2(L)$, showing the existence of a…