Diagrammes canoniques et representations modulo $p$ de $\GL_2(F)$

Abstract

Let $p$ be a prime number and $F$ a local field with residual characteristic $p$. In this article, to an irreducible smooth representation of $GL_2(F)$ over $\bar{\mathbf{F}}_p$ with central character, we associate canonically a diagram which determines the original representation up to isomorphism. We also determine it in some cases.