Modularity of some potentially Barsotti-Tate Galois representations

2002/05/18 by David Savitt, Savitt, David
Computer Science · Mathematics · #11F80 #14L15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT #msc:11F80 #msc:14L15

paper · pdf · doi:10.48550/arxiv.math/0205201

37 pages

openalex publication_date 2002/05/18 · arxiv created 2002/07/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a portion of a conjecture of B. Conrad, F. Diamond, and R. 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 integers of a local field. This makes crucial use of the filtered ϕ₁-modules of C. Breuil.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

Related

• Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture
• Modularity Lifting Theorems beyond the Taylor-Wiles Method. II
• The Breuil-M 'ezard conjecture for potentially Barsotti-Tate\n representations
• Local model theory for non-generic tame potentially Barsotti--Tate deformation rings
• On the Modularity of Wildly Ramified Galois Representations