Modularity of some potentially Barsotti-Tate Galois representations
Number Theory
2007-05-23 v3 Algebraic Geometry
Abstract
We prove a portion of a conjecture of B. Conrad, F. Diamond, and R. Taylor, yielding some new cases of the Fontaine-Mazur conjectures, specifically, the modularity of certain potentially Barsotti-Tate Galois representations. The proof follows the template of Wiles, Taylor-Wiles, and Breuil-Conrad-Diamond-Taylor, and relies on a detailed study of the descent, across tamely ramified extensions, of finite flat group schemes over the integers of a local field. This makes crucial use of the filtered \phi_1-modules of C. Breuil.
Cite
@article{arxiv.math/0205201,
title = {Modularity of some potentially Barsotti-Tate Galois representations},
author = {David Savitt},
journal= {arXiv preprint arXiv:math/0205201},
year = {2007}
}
Comments
37 pages