Finiteness properties of the category of mod $p$ representations of ${\mathrm{GL}}_2({\mathbb{Q}}_p)$

Abstract

We establish Bernstein-centre type of results for the category of mod $p$ representations of ${\mathrm{GL}}_2({\mathbb{Q}}_p)$. We treat all the remaining open cases, which occur when $p$ is $2$ or $3$. Our arguments carry over for all primes $p$. This allows us to remove the restrictions on the residual representation at $p$ in Lue Pan's recent proof of the Fontaine--Mazur conjecture for Hodge--Tate representations of $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ with equal Hodge--Tate weights.

minor changes after a referee report. Final version

References in corpus (1)

• Infinitesimal characters in arithmetic families

Cited by in corpus (1)

• On local Galois deformation rings