Controlling ramification in number fields
Abstract/Contents
- Abstract
- This thesis focuses on two aspects of limited ramification and is split up into two independent sections. The first section (which comprises the second and third chapters) is on the distribution of class groups of cyclic cubic fields. We propose an explanation for the discrepancy between the observed number of cyclic cubics whose 2-class group is C_2 x C_2 and the number predicted by the Cohen-Lenstra heuristics, in terms of an invariant living in a quotient of the Schur multiplier group. We also show that, in some cases, the definition of the invariant can be simplified greatly, and we compute 10^5 examples. The second section (which comprises the fourth and fifth chapters) discusses branched covers of algebraic curves, especially covers of elliptic curves with one branch point. We produce some techniques that allow us to write down explicit equations for such maps, and then we give examples of number fields which arise from such covers. Finally, we present some possibilities for future works that the author hopes to pursue.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Rubinstein-Salzedo, Simon |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Conrad, Brian, 1970- |
| Thesis advisor | Diaconis, Persi |
| Advisor | Conrad, Brian, 1970- |
| Advisor | Diaconis, Persi |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Simon Rubinstein-Salzedo. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Simon Rubinstein-Salzedo
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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