Mod p / p-adic local Langlands programs

 

Date: August 8 - 10, 2016         Place: Rm. 1423, KIAS, Seoul

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Speaker: Yongquan Hu (Universite de Rennes 1 / Morningside Center)
Title: Deformations of $Gal(bar{Q}_p/Q_p)$ and $GL_2(Q_p)$ representations
Abstract: Let $p$ be a prime number and $Q_p$ the field of $p$-adic numbers. In these lectures, I will first explain Colmez’s Montreal functor which relates $p$-adic/mod $p$ representations of $GL_2(Q_p)$ and of $Gal(bar{Q}_p/Q_p)$. This functor, together with the deformation-theoretic argument of Kisin, plays a key role in the construction of the $p$-adic local Langlands correspondence for $GL_2(Q_p)$. Finally, we will show how to use the correspondence to get information about the structure of deformation rings of $Gal(bar{Q}_p/Q_p)$, by working on the $GL_2(Q_p)$ side.


Speaker: Judith Ludwig (Universitat Bonn)

Title: Mod p Langlands correspondences via arithmetic geometry.
Abstract: In this minicourse we will study mod p Langlands type correspondences via arithmetic geometry.
I will begin by introducing the type of correspondences that we aim for and in particular the idea of a mod p local Langlands correspondence for GL(n). A candidate for this correspondence has recently been constructed by Scholze using the cohomology of the Lubin-Tate tower. After studying his construction I will explain some finer properties of the cohomology groups involved.