| Résume | Let $D$ be the non-split quaternion algebra over $\mathbb{Q}_p$. The classical Jacquet-Langlands correspondence relates irreducible complex representations of $D^{\times}$ with discrete series representations of $GL_2(\mathbb{Q}_p).$ About 10 years ago, using Lubin-Tate space, Scholze defined some interesting functors which gave a candidate for mod $p$ (and $p$-adic) Jacquet-Langlands correspondence, even for $GL_n$. We will talk about some results on Scholze functors in the case of $GL_2(\mathbb{Q}_p).$ The talk is based on joint works with Yongquan Hu. |
