Speaker
Benjamin Schraen
Description
In the hypothetical $p$-adic Langlands correspondence beyond the case of $GL_2$, the study of the finite slope locally analytic representations is, so far, the most accessible aspect. We can study locally analytic representations of $GL_n(\mathbb{Q}_p)$ appearing in the completed cohomology of Shimura varieties (or spaces of $p$-adic automorphic forms) and study their finite slope part. The description of this finite slope part can be done via the study of certain coherent sheaves on spaces of trianguline $p$-adic parameters. These coherent sheaves can be conjecturally described via a functor constructed by Bezrukavnikov. In this talk I will describe the context of this conjecture and explain the proof when $n=3$.