Conjectures about p-adic groups and their noncommutative geometry

Anne Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld

Research output: Chapter in Book/Report/Conference proceedingChapter

16 Scopus citations


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 for G, 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.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages37
StatePublished - 2017

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • General Mathematics


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