English

Modularity lifting theorems for Galois representations of unitary type

Number Theory 2019-02-20 v3 Representation Theory

Abstract

We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at l. This extends the results of Clozel, Harris and Taylor, and the subsequent work by Taylor. The proof uses the Taylor-Wiles method, as improved by Diamond, Fujiwara, Kisin and Taylor, applied to Hecke algebras of unitary groups, and results of Labesse on stable base change and descent from unitary groups to GL_n.

Keywords

Cite

@article{arxiv.0906.4189,
  title  = {Modularity lifting theorems for Galois representations of unitary type},
  author = {Lucio Guerberoff},
  journal= {arXiv preprint arXiv:0906.4189},
  year   = {2019}
}

Comments

32 pages, final version incorporating referee's suggestions

R2 v1 2026-06-21T13:16:46.641Z