Towards a Modulo p Langlands Correspondence for GL2

The authors construct new families of smooth admissible $overlinemathbbFp$-representations of $mathrmGL2(F)$, where $F$ is a finite extension of $mathbbQp$. When $F$ is unramified, these representations have the $mathrmGL2(mathcal OF)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.