The University of Southampton
University of Southampton Institutional Repository

Conjectures about p-adic groups and their noncommutative geometry

Conjectures about p-adic groups and their noncommutative geometry
Conjectures about p-adic groups and their noncommutative geometry
Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G.

At the heart of these conjectures are statements about the geometric structure of Bernstein components forG, both at the level of the space of irreducible representations and at the level of the associated Hecke algebras. We relate this to two well-known conjectures: the local Langlands correspondence and the Baum–Connes conjecture for G. In particular, we present a strategy to reduce the local Langlands correspondence for irreducible G-representations to the local Langlands correspondence for supercuspidal representations of Levi subgroups.
0271-4132
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4

Aubert, Anne-Marie, Baum, Paul, Plymen, Roger and Solleveld, Maarten (2017) Conjectures about p-adic groups and their noncommutative geometry Contemporary Mathematics (doi:10.1090/conm/691/13892).

Record type: Article

Abstract

Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G.

At the heart of these conjectures are statements about the geometric structure of Bernstein components forG, both at the level of the space of irreducible representations and at the level of the associated Hecke algebras. We relate this to two well-known conjectures: the local Langlands correspondence and the Baum–Connes conjecture for G. In particular, we present a strategy to reduce the local Langlands correspondence for irreducible G-representations to the local Langlands correspondence for supercuspidal representations of Levi subgroups.

PDF surveyAroundLLCv11.pdf - Accepted Manuscript
Available under License Other.
Download (1MB)

More information

Accepted/In Press date: 1 October 2016
Published date: 2017
Additional Information: ISBNs: 978-1-4704-3573-8 (print); 978-1-4704-4117-3 (online)
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 401084
URI: http://eprints.soton.ac.uk/id/eprint/401084
ISSN: 0271-4132
PURE UUID: ade9cddf-94b5-4cb7-9b6b-61c39e5d09c2

Catalogue record

Date deposited: 05 Oct 2016 10:48
Last modified: 17 Jul 2017 18:05

Export record

Altmetrics

Contributors

Author: Anne-Marie Aubert
Author: Paul Baum
Author: Roger Plymen
Author: Maarten Solleveld

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×