Geometric deformations of orthogonal and symplectic galois representations
Abstract/Contents
- Abstract
- For a representation of the absolute Galois group of the rationals over a finite field of characteristic p, we would like to know if there exists a lift to characteristic zero with nice properties. In particular, we would like it to be geometric in the sense of the Fontaine-Mazur conjecture: ramified at finitely many primes and potentially semistable at p. For two-dimensional representations, Ramakrishna proved that under technical assumptions odd representations admit geometric lifts. We generalize this to higher dimensional orthogonal and symplectic representations. The key ingredient is a smooth local deformation condition obtained by analysing unipotent orbits and their centralizers in the relative situation, not just over fields.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Booher, Jeremy |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Conrad, Brian |
| Thesis advisor | Conrad, Brian |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Yun, Zhiwei, 1982- |
| Advisor | Venkatesh, Akshay, 1981- |
| Advisor | Yun, Zhiwei, 1982- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jeremy Booher. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Jeremy Booher
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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