P-adic Hodge theory in rigid analytic families
Abstract/Contents
- Abstract
- In this thesis, we study p-adic Hodge theory in rigid analytic families. Roughly speaking, p-adic Hodge theory is the study of p-adic representations of p-adic Galois groups. One introduces certain p-adic period rings B, such as B_{HT}, B_{dR}, B_{st}, and B_{cris}, and uses them to define functors D_B(.) from the category of p-adic Galois representations to various categories of linear algebra data. In the first half of this thesis, we study generalizations of these functors to families of p-adic Galois representations with rigid analytic coefficients. We prove that the functors D_{HT}(.) and D_{dR}(.) are coherent sheaves, and we prove that the B-admissible locus is a closed subspace of the base. In the second half of this thesis, we study the linear algebra data which arises from families of potentially semi-stable Galois representations valued in a connected reductive group G. We prove that for any G, the moduli space of linear algebra data is reduced and locally a complete intersection, and we deduce that potentially semi-stable deformation rings are generically smooth and equi-dimensional.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Bellovin, Rebecca Michal |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Conrad, Brian, 1970- |
| Thesis advisor | Conrad, Brian, 1970- |
| Thesis advisor | McNamara, Peter |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Advisor | McNamara, Peter |
| Advisor | Venkatesh, Akshay, 1981- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Rebecca Michal Bellovin. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Rebecca Bellovin
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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