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dc.contributor.authorChen, Taoran
dc.date.accessioned2018-10-23T13:34:31Z
dc.date.available2018-10-23T13:34:31Z
dc.date.issued2018-08-30
dc.identifier.otherChen_cornellgrad_0058F_11098
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:11098
dc.identifier.otherbibid: 10489737
dc.identifier.urihttps://hdl.handle.net/1813/59641
dc.description.abstractSuppose ̄ρ: Gal( ̄F/F)→GL2(k)is a residual Galois representation satisfyingseveral mild conditions, whereFis a number field andkis a finite field withcharacteristicsp≥7. In this work, we show that for any finite flat reducedcomplete intersection overW(k),R, we can construct a deformation problemdefined by local conditions imposed on some finite set of places inF, such that thecorresponding universal deformation ring of ̄ρisR. It’s a theorem of Wiles that ifthe local conditions are chosen to express restriction to deformations coming frommodular forms, then the corresponding universal deformation ring is a finite flatreduced complete intersection, so our work can be regarded as a converse to Wiles’result.
dc.language.isoen_US
dc.subjectGalois representation
dc.subjectnumber theory
dc.subjectuniversal deformation ring
dc.subjectMathematics
dc.subjectdeformation theory
dc.titleAn Inverse Galois Deformation Problem
dc.typedissertation or thesis
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Mathematics
dc.contributor.chairRamakrishna, Ravi Kumar
dc.contributor.committeeMemberZywina, David J.
dc.contributor.committeeMemberTemplier, Nicolas P.
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/X43776Z9


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