Signs of a p-adic geometric Langlands correspondence: part II

Abstract: Recent developments in the geometrization of local Langlands correspondence suggests, among other things, that the category of smooth complex representations of a $p$-adic group can be embedded fully faithfully into a category of ind-coherent sheaves on a moduli space of Weil-Deligne representations. For the $p$-adic local Langlands correspondence, a geometric perspective is more speculative. In these talks we will outline the construction of a fully faithful contravariant embedding of the category of $p$-adic locally admissible representations of $\mathrm{GL}(2,\mathbb{Q}_p)$ into a suitable category of coherent sheaves on the moduli stack of 2-dimensional $p$-adic representations of $\mathrm{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)$. In this second talk in particular, we will emphasize the explicit and computable nature of the moduli stack of Galois representations and certain sheaves on it.

Attendance at the prior talk in this series will not be presumed.

This is joint work between Christian Johansson, James Newton and Carl Wang-Erickson.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.