An Inverse Galois Deformation Problem
| dc.contributor.author | Chen, Taoran | |
| dc.contributor.chair | Ramakrishna, Ravi Kumar | |
| dc.contributor.committeeMember | Zywina, David J. | |
| dc.contributor.committeeMember | Templier, Nicolas P. | |
| dc.date.accessioned | 2018-10-23T13:34:31Z | |
| dc.date.available | 2018-10-23T13:34:31Z | |
| dc.date.issued | 2018-08-30 | |
| 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.identifier.doi | https://doi.org/10.7298/X43776Z9 | |
| 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.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 | |
| dcterms.license | https://hdl.handle.net/1813/59810 | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Cornell University | |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Mathematics |
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