English

The inverse deformation problem

Rings and Algebras 2019-02-20 v2 Number Theory

Abstract

We show the inverse deformation problem has an affirmative answer: given a complete local noetherian ring AA with finite residue field k\pmb{k}, we show that there is a topologically finitely generated profinite group Γ\Gamma and an absolutely irreducible continuous representation ρˉ:ΓGLn(k)\bar\rho:\Gamma\to GL_n(\pmb{k}) such that AA is the universal deformation ring for Γ,ρˉ\Gamma,\bar\rho.

Keywords

Cite

@article{arxiv.1307.8356,
  title  = {The inverse deformation problem},
  author = {Timothy Eardley and Jayanta Manoharmayum},
  journal= {arXiv preprint arXiv:1307.8356},
  year   = {2019}
}

Comments

10 pages; statements corrected to exclude the case when the residual representation is $SL_3(\F_2)$

R2 v1 2026-06-22T01:01:32.039Z