A uniform bound for inertially equivalent, pure ℓ-adic representations: an extension of Faltings' theorem

2020/06/13 by Plawan Das, Das, Plawan, C. S. Rajan +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Primary 11F80 #Secondary 11G05. 11G10 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2006.07623

openalex publication_date 2020/06/13 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of inertial equivalence for integral ℓ-adic representation of the Galois group of a global field. We show that the collection of continuous, semisimple, pure ℓ-adic representations of the absolute Galois group of a global field lifting a fixed absolutely irreducible residual representation and with given inertial type outside a fixed finite set of places is uniformly bounded independent of the inertial type.

Related

• Lifting Galois representations over arbitrary number fields
• Distinguishing pure representations by normalized traces
• Finiteness theorems for potentially equivalent Galois representations: extension of Faltings' finiteness criteria
• Purity for families of Galois representations
• Quasi-semi-stable representations