2021/05/12 by Shaunak V. Deo, Deo, Shaunak V.
Mathematics · #11F25 #11F33(secondary) #11F80(primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2105.05823
openalex publication_date 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a continuous, odd, reducible and semi-simple 2-dimensional representation ρ0 of Gℚ,Np over a finite field of odd characteristic p, we study the relation between the universal deformation ring of the pseudo-representation corresponding to ρ0 (pseudo-deformation ring) and the big p-adic Hecke algebra to prove that the maximal reduced quotient of the pseudo-deformation ring is isomorphic to the local component of the big p-adic Hecke algebra corresponding to ρ0 if a certain global Galois cohomology group has dimension 1. This partially extends the results of Böckle to the case of residually reducible representations. We give an application of our main theorem to the structure of Hecke algebras modulo p. As another application of our methods and results, we prove a result about non-optimal levels of newforms lifting ρ0 in the spirit of Diamond-Taylor. This also gives a partial answer to a conjecture of Billerey-Menares.