Sur la présentation des représentations supersingulières de ${\mathrm{GL}}_2(F)$

Abstract

Let $F$ be a quadratic extension of ${\mathbb{Q}}_p$. We prove that smooth irreducible supersingular representations with central character of ${\mathrm{GL}}_2(F)$ are not of finite presentation.

19 pages, minor mistakes corrected, minor changes of notation