A note on some $p$-adic analytic Hecke actions

Lue Pan

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arXiv · 2012.11845

A note on some $p$-adic analytic Hecke actions

Lue Pan

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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 Gouv\^{e}a.

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Lue Pan. 2020-12-22. A note on some $p$-adic analytic Hecke actions. https://arxiv.org/abs/2012.11845

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