Haastert, Jeroen van (2023) CM-fields of degree 8 and their applications. Bachelor's Thesis, Mathematics.
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Abstract
The first chapter of this bachelor thesis covers basic results about number fields and complex multiplication fields (CM-fields). In chapter 2, it is discussed that equivalent ρ-structures yield equivalent results in regards to primitive CM-types and reflex fields. Chapter 3 contains the full classification of intermediate CM-fields, primitive CM-types and reflex fields for all Galois CM-fields of degree 8 and all possible ρ-structures. The next chapter covers a complete classification of all ρ- structures of abelian Galois groups of finite degree. Lastly, the obtained theory and results on CM-fields are put in practice by showing that the Jacobian J(C) is simple when C is given by η2 = (s + 2)(s8 − 8s6 + 20s4 − 16s2 + 2) or by the family of curves ym = xd + 1 with m > d primes such that m ≡ −1 (mod d).
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Kilicer, P. and Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 05 Jul 2023 12:31 |
| Last Modified: | 05 Jul 2023 12:31 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/30316 |
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