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

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 GL(2,Qp) into a suitable category of coherent sheaves on the moduli stack of 2-dimensional p-adic representations of Gal(Qp-bar/Qp), constructed by Wang-Erickson. We will also discuss analogous statements for SL(2,Qp), highlighting the role of endoscopy.

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)

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