Wiersema, Laurens (2026) Q-rational simple maximal CM points in the moduli space of principally polarized abelian varieties of dimension 4. Master's Thesis / Essay, Mathematics.
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Abstract
In this thesis, we show that there are exactly 5 cyclic octic CM fields with CM class number one, and that there are exactly 16 isomorphism classes of principally polarized simple abelian varieties of dimension 4 that have CM by the maximal order of one of these fields. In order to achieve this, we prove several properties of the rational primes that ramify in cyclic octic CM fields with CM class number one, and we find an upper bound on the conductor of such fields. We present an algorithm that uses these results to find the complete list of such fields.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Kilicer, P. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 17 Jul 2026 11:33 |
| Last Modified: | 17 Jul 2026 11:33 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37447 |
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