Kisin, Mark2017-07-112009Kisin, Mark. 2009. “Modularity of 2-Adic Barsotti-Tate Representations.” Inventiones Mathematicae 178 (3): 587–634.0020-99101432-1297http://nrs.harvard.edu/urn-3:HUL.InstRepos:33370067We prove a modularity lifting theorem for two dimensional, 2-adic, potentially Barsotti-Tate representations. This proves hypothesis (H) of Khare-Wintenberger, and completes the proof of Serre’s conjecture. The main new ingredient is a classification of connected finite flat group schemes over rings of integers of finite extensions of ℚ2.en-USJournal Article10.1007/s00222-009-0207-5