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.

arXiv comment12 pages, final version

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Cited by in corpus (4)

• Conjectures and results on modular representations of ${\mathrm{GL}}_n(K)$ for a $p$-adic field $K$
• On irreducible supersingular representations of ${\mathrm{GL}}_2(F)$
• Coherence of Augmented Iwasawa Algebras
• Iwahori-Hecke model for mod p representations of GL(2,F)