Modularity of some potentially Barsotti-Tate Galois representations

David Savitt

doi:10.1112/S0010437X03000289

Modularity of some potentially Barsotti-Tate Galois representations

David Savitt

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	31-63
Number of pages	33
Journal	Compositio Mathematica
Volume	140
Issue number	1
DOIs	https://doi.org/10.1112/S0010437X03000289
State	Published - Jan 2004
Externally published	Yes

Keywords

Breuil module
Galois representation
Modularity

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X03000289

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AB - 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.

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Modularity of some potentially Barsotti-Tate Galois representations

Abstract

Keywords

ASJC Scopus subject areas

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