An Inverse Galois Deformation Problem

dc.contributor.authorChen, Taoran
dc.contributor.chairRamakrishna, Ravi Kumar
dc.contributor.committeeMemberZywina, David J.
dc.contributor.committeeMemberTemplier, Nicolas P.
dc.date.accessioned2018-10-23T13:34:31Z
dc.date.available2018-10-23T13:34:31Z
dc.date.issued2018-08-30
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.identifier.doihttps://doi.org/10.7298/X43776Z9
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.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
dcterms.licensehttps://hdl.handle.net/1813/59810
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Mathematics
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