2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64101We 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 ϕ_1-modules of C. Breuil.37 pagesNumber TheoryAlgebraic Geometry11F80; 14L15text