A characterization of the relation between two \ℓ-modular\n correspondences

2019/11/28 by Robert Kurinczuk, Kurinczuk, Robert, Nadir Matringe +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1911.12891

openalex publication_date 2019/11/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Let F be a non archimedean local field of residual characteristic p and\n\ℓ a prime number different from p. Let \V denote Vign 'eras'\n\ℓ-modular local Langlands correspondence between irreducible\n\ℓ-modular representations of \GL_n(F) and n-dimensional\n\ℓ-modular Deligne representations of the Weil group \W_F. In a\nprevious work, enlarging the space of parameters to Deligne representations\nwith non necessarily nilpotent operators, we proposed a modification of the\ncorrespondence of Vign 'eras into a correspondence \C compatible with\nthe formation of local constants in the generic case. In this note, following a\nremark of Alberto M 'inguez, we characterize the modification \C\∘\n\V^-1 by a short list of natural properties.\n

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