Affine Deligne-Lusztig varieties of higher level and the local Langlands correspondence for GL₂

2015/04/01 by Alexander Ivanov, Ivanov, Alexander · 1 citation
Mathematics · #11F70 #11S37 #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT) #math.AG #math.RT #msc:11F70 #msc:11S37 #msc:14M15

paper · pdf · doi:10.48550/arxiv.1504.00264

37 pages

arxiv created 2015/04/01 · openalex publication_date 2015/04/01 · arxiv updated 2015/04/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In the present article we define coverings of affine Deligne-Lusztig varieties attached to a connected reductive group over a local field of characteristic p > 0. In the case of \GL₂, the unramified part of the local Langlands correspondence is realized in the ℓ-adic cohomology of these varieties. We show this by giving a detailed comparison with the realization of local Langlands via cuspidal types by Bushnell-Henniart. All proofs are purely local.

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