Bootsma, Sven (2020) Mordell’s Theorem Over Rational Function Fields Via Descent by 3-Isogeny. Bachelor's Thesis, Mathematics.
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Abstract
Mordell’s theorem states that the group of rational points on an elliptic curve Edefined over Q is a finitely generated abelian group. This thesis considers Mordell’s theorem over rational function fields of the form F_q(t), where q is a prime power. Assuming the existence of an F_q(t)-rational point of order 3 in E(F_q(t)), we prove this adaptation by performing an elementary descent by 3-isogeny. In the end we look at explicit examples for the rank of an elliptic curve over a rational function field.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 13 Jul 2020 13:50 |
| Last Modified: | 13 Jul 2020 13:50 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/22578 |
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