Trabajo Fin de Grado
El teorema de Nagell-Lutz
Autor/es | Cano Wall, Pablo |
Director | Tornero Sánchez, José María
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Departamento | Universidad de Sevilla. Departamento de Algebra |
Fecha de publicación | 2022-06-01 |
Fecha de depósito | 2023-02-21 |
Titulación | Universidad de Sevilla. Grado en Matemáticas |
Resumen | The goal of this memory is to prove the Nagell-Lutz theorem, an important theorem about the rational torsion of elliptic curves, which gives us a necessary condition
for a point to have finite order. To do this, we will ... The goal of this memory is to prove the Nagell-Lutz theorem, an important theorem about the rational torsion of elliptic curves, which gives us a necessary condition for a point to have finite order. To do this, we will start by studying the geometry of elliptic curves, how to endow them with an abelian group structure, the group formulas and some birational transformations that put the elliptic curve into the so-called Weierstrass normal form. Given an elliptic curve in Weierstrass normal form, we will show that if a point has finite order, then its coordinates must be integers, and we will summarize all the work in the proof of the theorem. |
Cita | Cano Wall, P. (2022). El teorema de Nagell-Lutz. (Trabajo Fin de Grado Inédito). Universidad de Sevilla, Sevilla. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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GM CANO WALL, PABLO.pdf | 2.689Mb | ![]() | Ver/ | |