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Modularity of 2-adic Barsotti-Tate representations

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We 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.

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  1. Department of Mathematics, University of Chicago, Chicago, IL, 060614, USA

    Mark Kisin

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  1. Mark Kisin
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Correspondence to Mark Kisin.

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The author was partially supported by NSF grant DMS-0400666 and a Sloan Research Fellowship.

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Kisin, M. Modularity of 2-adic Barsotti-Tate representations. Invent. math. 178, 587–634 (2009). https://doi.org/10.1007/s00222-009-0207-5

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