Theta Operator Equals Fontaine Operator on Modular Curves

2023/10/22 by Jiang, Yuanyang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.14243

Abstract

Inspired by [Pan22], we give a new proof that for an overconvergent modular eigenform f of weight 1+k with k∈ℤ_≥1, assuming that its associated global Galois representation ρ_f is irreducible, then f is classical if and only if ρ_f is de Rham at p. For the proof, we prove that theta operator θ^k coincides with Fontaine operator in a suitable sense.

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• On locally analytic vectors of the completed cohomology of modular curves II