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The inverse deformation problem

Part of: Structure and classification of infinite or finite groups Representation theory of groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  14 July 2016

Timothy Eardley  and
Jayanta Manoharmayum
Timothy Eardley
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK email pmp09tae@sheffield.ac.uk
Jayanta Manoharmayum*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK email J.Manoharmayum@sheffield.ac.uk
*
J.Manoharmayum@sheffield.ac.uk
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Abstract

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Given a commutative complete local noetherian ring $A$ with finite residue field $\boldsymbol{k}$ , we show that there is a topologically finitely generated profinite group $\unicode[STIX]{x1D6E4}$ and an absolutely irreducible continuous representation $\overline{\unicode[STIX]{x1D70C}}:\unicode[STIX]{x1D6E4}\rightarrow \text{GL}_{n}(\boldsymbol{k})$ such that $A$ is a universal deformation ring for $\unicode[STIX]{x1D6E4},\overline{\unicode[STIX]{x1D70C}}$ .

Keywords

inverse deformation problem

MSC classification

Primary: 20C20: Modular representations and characters 20E18: Limits, profinite groups 11F80: Galois representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 8 , August 2016 , pp. 1725 - 1739
Copyright
© The Authors 2016 

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