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Towards a Mod p Langlands Correspondence for GL2

Offered By: BIMSA via YouTube

Tags

Number Theory Courses Finite Fields Courses Representation Theory Courses Algebraic Geometry Courses Galois Representations Courses

Course Description

Overview

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Explore the intricacies of the mod $p$ Langlands correspondence in this one-hour lecture by Florian Herzig at BIMSA. Delve into an analog of the classical local Langlands correspondence, focusing on the relationship between Galois representations and representations of $p$-adic groups over characteristic $p$ coefficient fields. Examine the well-established case for $\mathrm{GL}_2(\mathbb Q_p)$ and investigate the challenges in extending this correspondence to other reductive groups, particularly $\mathrm{GL}_2(K)$ where $K$ is a nontrivial finite extension of $\mathbb Q_p$. Survey the current conjectures and recent advancements in the mod $p$ Langlands correspondence for $\mathrm{GL}_2(K)$, gaining insights into this open problem in modern number theory and representation theory.

Syllabus

Florian Herzig: Towards a mod $p$ Langlands correspondence for $\mathrm{GL}_2$ #ICBS2024


Taught by

BIMSA

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