The inverse problem for universal deformation rings and the special linear group
Representation Theory
2014-01-21 v2 Group Theory
Number Theory
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1308.1346,
title = {The inverse problem for universal deformation rings and the special linear group},
author = {Krzysztof Dorobisz},
journal= {arXiv preprint arXiv:1308.1346},
year = {2014}
}
Comments
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