Brauer classes, Azumaya algebras, and higher analogues
Abstract/Contents
- Abstract
- The Brauer group of a scheme has many interpretations. It is the group parameterizing both gerbes and Azumaya algebras over the scheme. It is also the group containing obstructions to the existence of universal sheaves. In this work, we extend both of these interpretations. In Chapter 2, we extend the understanding of the Brauer group in terms of Azumaya algebras to an understanding of the higher (third) cohomology group in terms of 2-Azumaya algebras. In Chapter 3, we use the interpretation of the Brauer group as obstructions to the existence of universal sheaves to study gerbes over genus 1 curves. This provides information about derived equivalences between connected components of the Picard stack of a genus 1 curve.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Taylor, Libby Riley |
|---|---|
| Degree supervisor | Vakil, Ravi |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Krashen, Daniel |
| Thesis advisor | Spink, Hunter |
| Degree committee member | Krashen, Daniel |
| Degree committee member | Spink, Hunter |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Libby Taylor. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/hy512zy5123 |
Access conditions
- Copyright
- © 2022 by Libby Riley Taylor
- License
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
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