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DC Field | Value | Language |
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dc.contributor.advisor | Dieulefait, L. V. (Luis Victor) | - |
dc.contributor.advisor | Freitas, Nuno | - |
dc.contributor.author | Sánchez Rodríguez, Ignasi | - |
dc.date.accessioned | 2023-04-17T09:00:23Z | - |
dc.date.available | 2023-04-17T09:00:23Z | - |
dc.date.issued | 2020-09-07 | - |
dc.identifier.uri | http://hdl.handle.net/2445/196845 | - |
dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2019-2020. Director: L. V. Dieulefait i Nuno Freitas | ca |
dc.description.abstract | In 1984, Jean-Pierre Serre, based on the ideas of Gerd Faltings, explained in his course at the Collège de France a method for comparing irreducible $\ell$-adic Galois representations. This method would later be anointed as the Faltings-Serre method by the mathematical community. In 1987 Ron Livné gave an algorithm to compare the case of 2-dimensional 2-adic Galois representations with even trace. In 2008 Gabriel Chênevert generalised it erasing the condition on the traces. In this thesis we are going to draw on his work to explore and formalise Serre’s ideas. In addition, we are going to collect some examples from Serre himself in the case of 2-dimensional 2-adic Galois representations from elliptic curves to understand the use of it and we are going to explain them in detail. Finally, we are also going to study Livné’s approach and give an example of this as well. | ca |
dc.format.extent | 75 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc by-nc-nd (c) Ignasi Sánchez Rodríguez, 2022 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Màster Oficial - Matemàtica Avançada | - |
dc.subject.classification | Teoria de Galois | cat |
dc.subject.classification | Corbes el·líptiques | cat |
dc.subject.classification | Treballs de fi de màster | cat |
dc.subject.classification | Anàlisi p-àdica | ca |
dc.subject.other | Galois theory | eng |
dc.subject.other | Elliptic curves | eng |
dc.subject.other | Master's theses | eng |
dc.subject.other | p-adic analysis | eng |
dc.title | Comparing Galois representations and the Faltings-Serre-Livné method | ca |
dc.type | info:eu-repo/semantics/masterThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
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tfm_sanchez_rodriguez_ignasi.pdf | Memòria | 1.11 MB | Adobe PDF | View/Open |
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