Moduli of finite flat group schemes, and modularity
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1085-1180
We prove that, under some mild conditions, a two dimensional $p$-adic Galois representation which is residually modular and potentially Barsotti-Tate at $p$ is modular. This provides a more conceptual way of establishing the Shimura-Taniyama-Weil conjecture, especially for elliptic curves which acquire good reduction over a wildly ramified extension of $\mathbb Q_3$. The main ingredient is a new technique for analyzing flat deformation rings. It involves resolving them by spaces which parametrize finite flat group scheme models of Galois representations.
@article{10_4007_annals_2009_170_1085,
author = {Mark Kisin},
title = {Moduli of finite flat group schemes, and modularity},
journal = {Annals of mathematics},
pages = {1085--1180},
year = {2009},
volume = {170},
number = {3},
doi = {10.4007/annals.2009.170.1085},
mrnumber = {2600871},
zbl = {1201.14034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.1085/}
}
TY - JOUR AU - Mark Kisin TI - Moduli of finite flat group schemes, and modularity JO - Annals of mathematics PY - 2009 SP - 1085 EP - 1180 VL - 170 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.1085/ DO - 10.4007/annals.2009.170.1085 LA - en ID - 10_4007_annals_2009_170_1085 ER -
Mark Kisin. Moduli of finite flat group schemes, and modularity. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1085-1180. doi: 10.4007/annals.2009.170.1085
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