Monodromy Groups of Supersingular Abelian Surfaces over ℚ_p

2025/11/27 by Chen, Moqing
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · doi:10.48550/arxiv.2511.22811

Abstract

For primes p≥ 7, we give a parametrization of the filtered φ-modules attached to the p-adic Tate modules of abelian surfaces over ℚ_p with supersingular good reduction. We use this classification to determine the neutral components of the monodromy groups of the associated p-adic representations up to ℚ_p-isomorphism. Furthermore, we analyze the p-adic distribution of these groups in the moduli space of filtered φ-modules. In particular, we prove that the neutral components are generically isomorphic to GL₂ ×_det GL₂.

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