An irreducibility criterion for group representations, with arithmetic applications

2010/02/16 by M. Longo, Longo, M., S. Vigni +1
Mathematics · #11F80 #20C12 #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #math.AC #math.NT #msc:11F80 #msc:20C12

paper · pdf · doi:10.48550/arxiv.1002.3150

11 pages

arxiv created 2010/02/16 · arxiv updated 2010/02/26

Abstract

We prove a criterion for the irreducibility of an integral group representation ρover the fraction field of a noetherian domain R in terms of suitably defined reductions of ρat prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.

Related

• Irreducibility Criteria for Local and Global Representations
• On deformation rings of residually reducible Galois representations and\n R=T theorems
• Residual irreducibility of compatible systems
• On irreducibility of induced modules and an adaptation of the Wigner--Mackey method of little groups
• Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,A)