Modularity of some potentially Barsotti-Tate Galois representations

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12 Scopus citations

Abstract

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 φ1-modules of Breuil.

Original languageEnglish (US)
Pages (from-to)31-63
Number of pages33
JournalCompositio Mathematica
Volume140
Issue number1
DOIs
StatePublished - Jan 2004

Keywords

  • Breuil module
  • Galois representation
  • Modularity

ASJC Scopus subject areas

  • Algebra and Number Theory

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