\(\ell\)-integral nonabelian Lubin-Tate theory
type: Item
instance of: scholarly article
title: \(\ell\)-integral nonabelian Lubin-Tate theory
zbMATH Open document ID: 1260.11070
DOI: 10.1215/00127094-1548425
published in: Duke Mathematical Journal
publication date: 2012-04-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.1887
full work available at URL: https://projecteuclid.org/euclid.dmj/1333633314
review text: For two primes \(\ell\neq p\), the author investigates the \(\mathbb {Z}_{\ell}\)-cohomology of the Lubin-Tate towers of a \(p\)-adic field. It realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible supercuspidal representations parameterized by a \(\mathbb {Z}_{\ell}\)-algebra \(R\) in a way compatible with the extension of scalars. Applied to \(R=\overline{ \mathbb {F}}_{\ell}\), this gives a cohomological realization of the Langlands-Vigneras correspondence for supercuspidals and a new proof of its existence. Applied to complete local algebras, this provides bijections between deformations of matching \(\overline{ \mathbb {F}}_{\ell}\)-representations. Besides, a virtual realization of both the semi-simple Langlands-Vigneras correspondence and the \(\ell\)-modular Langlands-Jacquet transfer for all representations is obtained, by using the cohomology complex and working in a suitable Grothendieck group.
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 14G35
zbMATH DE Number: 6029036
author: J.-F. Dat
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
OpenAlex ID: W1525661960
arXiv ID: 1011.1887
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description: scientific article; zbMATH DE number 6029036