The inverse problem for universal deformation rings and the special linear group

2013/08/06 by Krzysztof Dorobisz, Dorobisz, Krzysztof
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.GR #math.NT #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1308.1346

Paper structured in a new way, results unchanged. Improved exposition, some proofs altered, additional remarks added. Last section made more precise. Similar results have been independently obtained by Eardley and Manoharmayum in their ArXiv:1307.8356 preprint

arxiv created 2013/12/06 · arxiv updated 2014/01/21

Abstract

We show that every complete noetherian local commutative ring R with residue field k can be realized as a universal deformation ring of a continuous linear representation of a profinite group. More specifically, R is the universal deformation ring of the natural representation of SL_n(R) in SL_n(k), provided that n is at least 4. We also check for which R an analogous result is true in case n=2 and n=3.

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