Kisin, Mark2015-03-132009Kisin, Mark. 2009. “Moduli of Finite Flat Group Schemes, and Modularity.” Annals of Mathematics 170, no. 3: 1085–1180.0003-486Xhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:14168859We 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 ℚ3. 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.en-USJournal Article2015-03-1310.4007/annals.2009.170.1085