Hattum, Mariska van (2023) Brauer groups and the Brauer-Manin obstruction. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis, the ultimate goal is to introduce the Brauer group of a variety and understand how it can be used to detect an obstruction to the Hasse principle. We provide an overview of the fundamental theory, including the necessary background in advanced algebra, algebraic geometry, and number theory. In the central part of this paper, we study the Brauer groups of fields, rings, and varieties, without introducing cohomology. The theory is applied to an example of a surface first considered by Swinnerton-Dyer. We conclude by confirming that for this example, despite the presence of points everywhere locally, there is a Brauer-Manin obstruction to the presence of global points.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Salgado Guimaraes da Silva, C. and Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 20 Jul 2023 12:59 |
| Last Modified: | 20 Jul 2023 12:59 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/30819 |
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