Spaces of modular forms. Modular curves and dimensions

The Modularity Theorem states that all rational elliptic curve arise from modular forms. In 1995, Andrew Wiles proved a special case of this theorem (then known as the Taniyama–Shimura conjecture) for semistable elliptic curves, completing the proof of Fermat’s Last Theorem after some 350 years. Lat...

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Detalles Bibliográficos
Autor: López Sánchez, Jesús
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/93643
Acceso en línea:https://hdl.handle.net/11441/93643
Access Level:acceso abierto
Palabra clave:Modularidad, Teorema de
Descripción
Sumario:The Modularity Theorem states that all rational elliptic curve arise from modular forms. In 1995, Andrew Wiles proved a special case of this theorem (then known as the Taniyama–Shimura conjecture) for semistable elliptic curves, completing the proof of Fermat’s Last Theorem after some 350 years. Later, Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor extended Wiles’s techniques to prove completely the Modularity Theorem. In this work we explain a complex analytic version of this notable theorem.

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