Taams, Lucas (2025) Properness of schemes and compactness of sets of rational points. Master's Thesis / Essay, Mathematics.
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Abstract
We define the fine topology on X(R) given a scheme X and a ring with topology R and outline important properties from [5] and prove new properties. We restate the theorem of equivalence of proper and compactness of schemes for local fields and prove a theorem of such equivalence for global fields in terms of adeles. It is shown that proper-to-compact results for topological fields can only hold if the field is a local field. A generalization of properness to compactness for a class of local topological rings is proven. A generalization of compactness to properness is proven for Henselian fields. Both these proofs closely follow the proof technique from [4].
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Lorscheid, O. and Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 28 Jan 2025 09:33 |
| Last Modified: | 28 Jan 2025 09:33 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/34613 |
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