The ℓ-modular local Langlands correspondence and local factors

2018/05/15 by Robert Kurinczuk, Kurinczuk, Robert, Nadir Matringe +1
Mathematics · #11F70 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1805.05888

openalex publication_date 2018/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-archimedean local field of residual characteristic p, ℓ≠ p be a prime number, and W_F the Weil group of F. We classify the indecomposable W_F-semisimple Deligne \mathbbF_ℓ-representations in terms of the irreducible \mathbbF_ℓ-representations of W_F, and extend constructions of Artin-Deligne local factors to this setting. Finally, we define a variant of the ℓ-modular local Langlands correspondence which satisfies a preservation of local factors statement for generic representations.

Citations

• Deligne--Langlands gamma factors in families

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