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Title: La corba de Frey: teoria i aplicacions
Author: Curcó Iranzo, Mar
Director/Tutor: Travesa i Grau, Artur
Keywords: Corbes el·líptiques
Treballs de fi de grau
Superfícies cúbiques
Anàlisi diofàntica
Funcions modulars
Elliptic curves
Bachelor's thesis
Cubic surfaces
Diophantine analysis
Modular functions
Issue Date: 29-Jun-2017
Abstract: [en] We start this thesis with a brief study on the Rieman-Roch Theorem so we can later introduce the concept of elliptic curve. We’ll proceed studying these as Weirstrass plane cubics and their reduction behaviour. Subsequently we’ll develop the construction of Frey’s curve and study some of its properties. Then, we give a short introduction to modular functions and Galois representation. Finally, we draw an outline for the proof of Fermat’s Theorem, where we can appreciate the importance of said curve. We conclude with an application of this method on other diofantic equations.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Artur Travesa i Grau
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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