Non-minimal modularity lifting in weight one

2015/01/30 by Calegari, Frank
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1502.00029

Abstract

We prove an integral R = T theorem for odd two dimensional p-adic representations of the absolute Galois group which are unramified at p, extending results of [CG] to the non-minimal case. We prove, for any p, the existence of Katz modular forms modulo p of weight one which do not lift to characteristic zero.

Related

• R=T theorems for weight one modular forms
• Dihedral Galois representations and Katz modular forms
• Minimal modularity lifting for GL2 over an arbitrary number field
• Modularity Lifting beyond the Taylor-Wiles Method
• Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case