Lifting irreducible Galois representations

2018/10/13 by Najmuddin Fakhruddin, Fakhruddin, Najmuddin, Chandrashekhar Khare +3 · 1 citation
Computer Science · Mathematics · #11F80 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11F80

paper · pdf · doi:10.48550/arxiv.1810.05803

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arxiv created 2018/10/13 · openalex publication_date 2018/10/13 · arxiv updated 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd representations satisfying local ramification hypotheses and a certain multiplicity-free condition on the adjoint representation admit geometric lifts. For general number fields, we show without any oddness or multiplicity condition that the representation admits a p-adic lift if it does everywhere locally.

Citations

• On the automorphy of l-adic Galois representations with small residual image
• Modular Elliptic Curves and Fermat's Last Theorem
• Compatible systems of Galois representations associated to the exceptional group E6

Cited by

• Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations

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