$p$-adic local Langlands correspondence and weight shifting
type: Item
instance of: scholarly article
title: $p$-adic local Langlands correspondence and weight shifting
zbMATH Open document ID: 1470.11304
DOI: 10.4171/JEMS/851
author: Pierre Colmez
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2019-03-14T00:00:00Z
review text: Summary: If \(f\) is a modular form of weight \(\geq 2\), the representation of \(\mathrm {GL}_2(\mathbb Q_p)\) attached to it by the \(p\)-adic local Langlands correspondence encodes the representation attached by the classical correspondence. We introduce weight shifting techniques that allow us to extend the result to weight 1. We also give a full description of the Jordan-Hölder components of the locally analytic representations appearing in the correspondence.
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 7036222
zbMATH Keywords: local Langlands correspondence
zbMATH Keywords: weight 1 modular form
zbMATH Keywords: locally analytic representation
zbMATH Keywords: Kirillov model
zbMATH Keywords: Drinfeld upper half-plane
zbMATH Keywords: Breuil-Strauch conjecture
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/jems/851
OpenAlex ID: W2902905649
description: scientific article; zbMATH DE number 7036222