dc.contributor.author Chen, Taoran dc.date.accessioned 2018-10-23T13:34:31Z dc.date.available 2018-10-23T13:34:31Z dc.date.issued 2018-08-30 dc.identifier.other Chen_cornellgrad_0058F_11098 dc.identifier.other http://dissertations.umi.com/cornellgrad:11098 dc.identifier.other bibid: 10489737 dc.identifier.uri https://hdl.handle.net/1813/59641 dc.description.abstract Suppose $\bar{\rho}: \Gal({\bar{F}/F}) \rightarrow \GL_2(\mathbf{k})$ 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.iso en_US dc.subject Galois representation dc.subject number theory dc.subject universal deformation ring dc.subject Mathematics dc.subject deformation theory dc.title An Inverse Galois Deformation Problem dc.type dissertation or thesis thesis.degree.discipline Mathematics thesis.degree.grantor Cornell University thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Mathematics dc.contributor.chair Ramakrishna, Ravi Kumar dc.contributor.committeeMember Zywina, David J. dc.contributor.committeeMember Templier, Nicolas P. dcterms.license https://hdl.handle.net/1813/59810 dc.identifier.doi https://doi.org/10.7298/X43776Z9
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