Moduli of Fontaine--Laffaille representations and a mod-p local-global compatibility result

2021/09/06 by Daniel Le, Le, Daniel, Bao V. Le Hung +7
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2109.02720

openalex publication_date 2021/09/06 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

Let F/F⁺ be a CM field and let \widetildev be a finite unramified place of F above the prime p. Let r: Gal(ℚ/F)→ GL_n(\mathbbF_p) be a continuous representation which we assume to be modular for a unitary group over F⁺ which is compact at all real places. We prove, under Taylor--Wiles hypotheses, that the smooth GL_n(F_\widetildev)-action on the corresponding Hecke isotypical part of the mod-p cohomology with infinite level above \widetildev|_F⁺ determines r|_Gal(ℚ_p/F_\widetildev), when this latter restriction is Fontaine--Laffaille and has a suitably generic semisimplification.

Citations

• On mod local-global compatibility for in the ordinary case

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• Multiplicities in the ordinary part of mod p cohomology for GL_n(ℚ_p)