On the rank of the multivariable (φ,O_K^×)-modules associated to mod p representations of GL₂(K)

2024/03/30 by Yitong Wang, Wang, Yitong
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2404.00389

Abstract

Let p be a prime number, K a finite unramified extension of ℚ_p and \mathbbF a finite extension of \mathbbF_p. For π an admissible smooth representation of GL₂(K) over \mathbbF satisfying certain multiplicity-one properties, we compute the rank of the associated étale (φ,O_K^×)-module D_A(π) defined by Breuil-Herzig-Hu-Morra-Schraen, extending their results.

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