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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 $\bar{\rho}: \Gal({\bar{F}/F}) \rightarrow \GL_2(\mathbf{k})$ is a residual Galois representation satisfying several mild conditions, where $F$ is a number field and $\mathbf{k}$ is a finite field with characteristics $p \geq 7$. In this work, we show that for any finite flat reduced complete intersection over $W(\mathbf{k})$, $\mathcal{R}$, we can construct a deformation problem defined by local conditions imposed on some finite set of places in $F$, such that the corresponding universal deformation ring of $\bar{\rho}$ is $\mathcal{R}$. It's a theorem of Wiles that if the local conditions are chosen to express restriction to deformations coming from modular forms, then the corresponding universal deformation ring is a finite flat reduced 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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