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Inverse Deformation Problems for Special Linear and Symplectic groups

Eardley, Timothy (2015) Inverse Deformation Problems for Special Linear and Symplectic groups. PhD thesis, University of Sheffield.

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Abstract

The principal result of this thesis is an affirmative answer to the inverse deformation problem which asks: Does a given complete noetherian local ring have a realisation as the unrestricted universal deformation ring of any residual representation? This is proved in two ways: firstly a complete answer is given using the family of special linear groups over complete noetherian local rings and secondly, if the finite field does not have 3 elements or does not have characteristic 2, it is answered using the family of symplectic groups. Of central importance to the result in the symplectic case is the establishment of a structure theorem for subgroups of special linear groups which surject onto symplectic groups over finite fields.

Item Type: Thesis (PhD)
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Identification Number/EthosID: uk.bl.ethos.680587
Depositing User: Mr Timothy Eardley
Date Deposited: 15 Mar 2016 13:10
Last Modified: 03 Oct 2016 13:09
URI: http://etheses.whiterose.ac.uk/id/eprint/12181

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