Evink, Tim (2020) Two-descent on hyperelliptic curves of genus 2. Master's Thesis / Essay, Mathematics.
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Abstract
In this thesis the theory of two-descent is treated for Jacobians of hyperelliptic curves of odd degree. Then the theory is applied in various ways to the family of genus 2 curves determined by the equation y^2=x(x^2-p^2)(x^2-4p^2), where p is a prime not 2 or 3. We are able to prove that various infinite collections of primes exist for which the Jacobian has non-trivial 2-torsion. In particular, it is shown that for infinitely many primes, the 2-torsion of Tate-Shafarevich group has order 16.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Top, J. and Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 04 Mar 2020 13:43 |
| Last Modified: | 04 Mar 2020 13:43 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/21636 |
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