Theta operator equals Fontaine operator on modular curves
Abstract
Inspired by [Pan26], we give a new proof that for an overconvergent modular eigenform f of weight 1 + k with k ∈ ℤ ≥ 1 , assuming that its associated Galois representation ρ f : Gal ℚ → GL 2 ( ℚ ¯ p ) is irreducible, then f is classical if and only if the associated Galois representation 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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Mathematical functions and polynomials
Publication details
- Journal / source
- Journal de l’École polytechnique — Mathématiques
- Volume
- 13
- Pages
- 349–398
- Publication date
- 2 February 2026
- Language
- EN