Coefficient systems and supersingular representations of GL₂(F)

2004/03/15 by Vytautas Paškūnas, Vytautas Paskunas, Paskunas, Vytautas · 1 citation
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.math/0403240

90 pages

arxiv created 2004/03/15 · openalex publication_date 2004/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-Archimedean local field with the residual characteristic p. We construct a "good" number of smooth irreducible F_p-representations of GL₂(F), which are supersingular in the sense of Barthel and Livné. If F=Q_p then results of Breuil imply that our construction gives all the supersingular representations up to the twist by an unramified quasi-character. We conjecture this is true for arbitrary F.

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