Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian
Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait
| Autor: | |
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| Formato: | tesis de maestría |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/129003 |
| Acesso em linha: | https://hdl.handle.net/2445/129003 |
| Access Level: | acceso abierto |
| Palavra-chave: | Darrer teorema de Fermat Cossos algebraics Treballs de fi de màster Nombres primers Corbes el·líptiques Geometria algebraica aritmètica Fermat's last theorem Algebraic fields Master's theses Prime numbers Elliptic curves Arithmetical algebraic geometry |
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Fermat’s last theorem: work of Kummer, Furtwängler and TerjanianMoya Viñas, AdrianaDarrer teorema de FermatCossos algebraicsTreballs de fi de màsterNombres primersCorbes el·líptiquesGeometria algebraica aritmèticaFermat's last theoremAlgebraic fieldsMaster's thesesPrime numbersElliptic curvesArithmetical algebraic geometryTreballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait[en] As it is well-known, Fermat’s Last Theorem states that the equation $x^{n} + y^{n} = z^{n}, yxz\neq 0$ has no integer solutions when the exponent n is greater or equal than 3. It was enunciated by Fermat around 1630 and stood unsolved for more than 350 years, until 1994 Andrew Wiles finally took that last step by proving the modularity conjecture for semistable elliptic curves. This thesis highlights the first steps taken in proving the theorem, before the use of elliptic curves and modularity. Our objective is to resume all these results and try to give a general point of view of what was known before the use of modern methods. Starting with elementary results, we move on to see Kummer’s proof for regular primes. Afterwards, we see how Furtwängler uses class field theory to work on Fermat’s problem, and give us more partial results of the theorem. Finally we study a generalization of Fermat’s last theorem for even exponent, due to Hellegouarch, using again the techniques of class field theory.Dieulefait, L. V. (Luis Victor)2018info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/129003Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc-by-nc-nd (c) Adriana Moya Viñas, 2018http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1290032026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| title |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| spellingShingle |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian Moya Viñas, Adriana Darrer teorema de Fermat Cossos algebraics Treballs de fi de màster Nombres primers Corbes el·líptiques Geometria algebraica aritmètica Fermat's last theorem Algebraic fields Master's theses Prime numbers Elliptic curves Arithmetical algebraic geometry |
| title_short |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| title_full |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| title_fullStr |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| title_full_unstemmed |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| title_sort |
Fermat’s last theorem: work of Kummer, Furtwängler and Terjanian |
| dc.creator.none.fl_str_mv |
Moya Viñas, Adriana |
| author |
Moya Viñas, Adriana |
| author_facet |
Moya Viñas, Adriana |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Dieulefait, L. V. (Luis Victor) |
| dc.subject.none.fl_str_mv |
Darrer teorema de Fermat Cossos algebraics Treballs de fi de màster Nombres primers Corbes el·líptiques Geometria algebraica aritmètica Fermat's last theorem Algebraic fields Master's theses Prime numbers Elliptic curves Arithmetical algebraic geometry |
| topic |
Darrer teorema de Fermat Cossos algebraics Treballs de fi de màster Nombres primers Corbes el·líptiques Geometria algebraica aritmètica Fermat's last theorem Algebraic fields Master's theses Prime numbers Elliptic curves Arithmetical algebraic geometry |
| description |
Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait |
| publishDate |
2018 |
| dc.date.none.fl_str_mv |
2018 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| format |
masterThesis |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/129003 |
| url |
https://hdl.handle.net/2445/129003 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.rights.none.fl_str_mv |
cc-by-nc-nd (c) Adriana Moya Viñas, 2018 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
cc-by-nc-nd (c) Adriana Moya Viñas, 2018 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.source.none.fl_str_mv |
Màster Oficial - Matemàtica Avançada reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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|
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|
| _version_ |
1869413896314421248 |
| score |
15,301629 |