Dijk, Ruben van (2024) On Howard's Kolyvagin systems for residue characteristic 2. Master's Thesis / Essay, Mathematics.
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Abstract
In [How04] Howard reformulates Kolyvagin’s proof [Kol89] of the bound on the p-Selmer group of an elliptic curve in a modern style, strengthening Kolyvagin’s bound on the annihilator to a bound on the length; however, Howard omits the case where p = 2. In this thesis we discuss Howard’s proof in detail, and in an attempt to generalize his results to all primes p, study where his proofs break down when p = 2. We find that under the assumption of two technical conjectures, a similar but weaker bound applies to the length of the 2-Selmer group.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Keller, T. and Muller, J.S. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 13 Aug 2024 09:27 |
| Last Modified: | 13 Aug 2024 09:27 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33941 |
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