Posthumus, Max (2023) Computing the torsion subgroup of Jacobian surfaces over number fields. Master's Thesis / Essay, Mathematics.
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Abstract
We describe and prove the correctness of an algorithm that theoretically computes the K-rational torsion subgroup of an abelian variety defined over a number field K. We make this concrete for Jacobians of genus 2 curves over number fields and implement this in Magma. The algorithm is largely based on work by Michael Stoll. Using this algorithm we look into various applications, such as finding unknown torsion structures and finding isogenies between abelian varieties.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Muller, J.S. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 13 Nov 2023 13:46 |
| Last Modified: | 13 Nov 2023 13:46 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/31630 |
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