R=T theorems for weight one modular forms

2022/03/17 by Tobias Berger, Berger, Tobias, Krzysztof Klosin +1
Mathematics · #11F33 #11F80 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2203.09434

openalex publication_date 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove modularity of certain residually reducible ordinary 2-dimensional p-adic Galois representations with determinant a finite order odd character χ. For certain non-quadratic χ we prove an R=T result for T the weight 1 specialisation of the Hida Hecke algebra acting on non-classical weight 1 forms, under the assumption that no two Hida families congruent to an Eisenstein series cross in weight 1. For quadratic χ we prove that the quotient of R corresponding to deformations split at p is isomorphic to the Hecke algebra acting on classical CM weight 1 modular forms.

Related

• Non-minimal modularity lifting in weight one
• Classical forms of weight one in ordinary families
• On Galois Representations of Weight One
• Traces on Hecke algebras and families of p-adic modular forms
• Hecke stability and weight 1 modular forms