Lifting Galois representations via Galois cohomology

2025/08/13 by Mathieu Florence, Florence, Mathieu
Computer Science · Engineering · Mathematics · #12G05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.2508.09739

openalex publication_date 2025/08/13 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

This is a survey paper, on recent progress around lifting Galois representations. I focused on approaches that solely rely on Galois cohomology. Emphasis is laid on material I talked about, at the conference held in Ottawa in June 2024, to celebrate Ján Mináč's 71th birthday.

Citations

• The lifting problem for Galois representations
• Galois representations modulo p that do not lift modulo p²
• Lifting Galois representations via Kummer flags
• Smooth profinite groups, II: the Uplifting Pattern
• Liftable groups, negligible cohomology and Heisenberg representations
• Lifting low-dimensional local systems
• Lifting vector bundles to Witt vector bundles

Related

• Lifting Galois representations over arbitrary number fields
• The lifting problem for Galois representations
• Galois representations
• The Unreasonable Efficacy of the Lifting Condition in Higher Categorical Galois Theory I: a Quasi-categorical Galois Theorem
• Deformations of Galois representations and exceptional monodromy, II:\n raising the level