Note on a certain category of mod p representations

2025/03/22 by Sorgdrager, Reinier
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.17773

Abstract

Let p>3 be a prime number, f≥1 an integer. We consider a certain full subcategory \mathcal C of the category of smooth admissible mod p representations of either GL₂\mathbf Q_p^f or of the group of units of the quaternion algebra over \mathbf Q_p^f. This category was introduced in the context of the mod p Langlands program by Breuil-Herzig-Hu-Morra-Schraen in the GL₂-case and by Hu-Wang in the quaternion case. We prove that whether a smooth admissible mod p representation π (with central character) belongs to \mathcal C is completely determined by the restriction of π to an arbitrarily small open subgroup.

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