A note on some p-adic analytic Hecke actions

2020/12/22 by Lue Pan, Pan, Lue
Mathematics · #11F33 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.11845

openalex publication_date 2020/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the action of Hecke operators away from p on the space of (p-adic) overconvergent modular forms is (p-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended naturally to an action of rigid functions on its generic fiber. This directly determines the Hodge-Tate-Sen weights of Galois representation associated to an overconvergent eigenform and confirms a conjecture of Gouvêa.

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