Conjectures about 𝑝-adic groups and their noncommutative geometry

DOI10.1090/conm/691/13892zbMath1468.22020arXiv1508.02837OpenAlexW2963736306MaRDI QIDQ4635104

Paul F. Baum, Roger Plymen, Maarten Solleveld, Anne-Marie Aubert

Publication date: 13 April 2018

Published in: Around Langlands Correspondences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.02837

zbMATH Keywords

local Langlands correspondenceirreducible representationsBaum-Connes conjectureconjecturesreductive \(p\)-adic groupsassociated Hecke algebrasgeometric structure of Bernstein components

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Langlands-Weil conjectures, nonabelian class field theory (11S37) Linear algebraic groups over local fields and their integers (20G25) Equivariant (K)-theory (19L47)

Related Items (12)

Endomorphism algebras and Hecke algebras for reductive \(p\)-adic groups ⋮ Generalizations of the Springer correspondence and cuspidal Langlands parameters ⋮ Centralisers, complex reflection groups and actions in the Weyl group \(E_6\) ⋮ A local Langlands correspondence for unipotent representations ⋮ Hecke algebras for \(p\)-adic reductive groups and local Langlands correspondences for Bernstein blocks ⋮ On unipotent representations of ramified 𝑝-adic groups ⋮ Coherent Springer theory and the categorical Deligne-Langlands correspondence ⋮ Some aspects of the geometric structure of the smooth dual of $p$-adic reductive groups ⋮ Affine Hecke algebras and their representations ⋮ Around the Langlands program ⋮ Regular Bernstein blocks ⋮ Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups (with an appendix by Jessica Fintzen)

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