On the mordell - Weil rank of hyperelliptic curves
| dc.contributor.advisor | Masdeu Sabaté, Marc | |
| dc.contributor.author | Mata Carmona, Guillem | |
| dc.date.accessioned | 2026-07-13T08:45:22Z | |
| dc.date.available | 2026-07-13T08:45:22Z | |
| dc.date.issued | 2026-06-12 | |
| dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2026. Director: Marc Masdeu Sabaté | |
| dc.description.abstract | The Jacobian of an algebraic curve C defned over a number feld K is an abelian variety whose group of K-rational points has finite rank, by the Mordell-Weil theorem. We study the proof of this theorem and the problem of computing the rank. We give some bounds on this rank in a certain family of curves by studying the Selmer group, which is a cohomological device that can be explicitly computed. | |
| dc.format.extent | 68 p. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/2445/230622 | |
| dc.language.iso | eng | |
| dc.rights | cc by-nc-nd (c) Mata Carmona, Guillem, 2026 | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ca | |
| dc.source | Màster Oficial - Matemàtica Avançada | |
| dc.subject.classification | Corbes algebraiques | |
| dc.subject.classification | Geometria algebraica | |
| dc.subject.classification | Corbes modulars | |
| dc.subject.classification | Treballs de fi de màster | |
| dc.subject.other | Algebraic curves | |
| dc.subject.other | Algebraic geometry | |
| dc.subject.other | Modular curves | |
| dc.subject.other | Master's thesis | |
| dc.title | On the mordell - Weil rank of hyperelliptic curves | |
| dc.type | info:eu-repo/semantics/masterThesis |
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