Symplectic representations of inertia groups

2000/09/02 by A. Silverberg, Alice Silverberg, Silverberg, A. +2
Mathematics · #11E95 #11S23 #20C11 #20G25 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #Number Theory (math.NT) #math.GR #math.NT #msc:11E95 #msc:11S23 #msc:20C11 #msc:20G25

paper · pdf · doi:10.48550/arxiv.math/0009024

LaTeX2e, 7 pages

arxiv created 2000/09/02 · openalex publication_date 2000/09/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose ℓ is a prime number, ℓ >3, K is a field that is an unramified finite extension of the field \Q_ℓ of ℓ-adic numbers, and G is a finite group that is a semi-direct product of a normal ℓ'-subgroup H and a cyclic ℓ-group L. Suppose that the group algebra K[H] is decomposable. If there exists an embedding of G in the symplectic group \Sp_2d(K) for some positive integer d, then there exists an embedding of G in \Sp_2d(\mathcal O_K), where \mathcal O_K is the ring of integers of K.

Related

• The Realizability Problem with Inertia Conditions
• Polarizations on abelian varieties and self-dual ell-adic representations of inertia groups
• Modular representations arising from self-dual ℓ-adic representations of finite groups
• The (p,t,a)-inertial groups as finite monodromy groups
• A uniform bound for inertially equivalent, pure ℓ-adic representations: an extension of Faltings' theorem