EVENT DETAILS AND ABSTRACT

Title: Diagrams and mod p representations
Speaker: Haoran Wang
Speaker Info: Michigan State University
Brief Description:
Special Note:
Abstract:

Let $p>2$ be a prime number and $L$ be a finite unramified extension of $\mathbb{Q}_p.$ To every two dimensional 'generic' local Galois representation $\overline{\rho}_p$ of $Gal(\overline{L}/L)$ over $\overline{\mathbb{F}}_p,$ Breuil and Paskunas has associated an (infinite) family of smooth admissible $\overline{\mathbb{F}}_p$-representations of $GL_2(L)$ via the 'diagrams' . When $\overline{\rho}_p$ comes from a global modular mod $p$ Galois representation $\overline{\rho}$, Emerton, Gee and Savitt showed that the $p$ component $\pi_p(\overline{\rho})$ of the mod $p$ automorphic representation associated to $\overline{\rho}$ belongs to Breuil-Paskunas' family. In this talk, I will explain how to deduce the $1+p M_2(O_L)$-invariants of $\pi_p(\overline{\rho})$ from Emerton-Gee-Savitt's work in the case where $\overline{\rho}_p$ is semisimple, hence gives a further restriction on a possible mod $p$ correspondence. This is a work in progress with Yongquan Hu.