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Modularity of some potentially Barsotti–Tate Galois representations

Published online by Cambridge University Press:  04 December 2007

David Savitt
Affiliation:
Department of Mathematics, McGill University, 805 Sherbrooke W., Montréal, Québec, Canada H3A 2K6 dsavitt@math.mcgill.ca
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Abstract

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We prove a portion of a conjecture of Conrad, Diamond, and 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 ring of integers of a local field. This makes crucial use of the filtered $\phi_1$-modules of Breuil.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2004
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