A note on presentations of supersingular representations of ${\text{GL}}_2(F)$

Abstract

We prove that any smooth irreducible supersingular representation with central character of ${\text{GL}}_2(F)$ is never of finite presentation when $F$ is a finite field extension of ${\mathbb{Q}}_p$ such that $F\ne {\mathbb{Q}}_p$, extending a result of Schraen for quadratic extensions.

12 pages, final version