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Explicit class field theory via elliptic curves

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dc.contributor Guitart Morales, Xavier
dc.creator Gil Muñoz, Daniel
dc.date 2018-03-27T09:11:05Z
dc.date 2018-03-27T09:11:05Z
dc.date 2017-09-10
dc.date.accessioned 2024-12-16T10:26:20Z
dc.date.available 2024-12-16T10:26:20Z
dc.identifier http://hdl.handle.net/2445/121135
dc.identifier.uri http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/20940
dc.description Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Xavier Guitart Morales
dc.description [en] We present and describe a proof due to Deuring of the Hilbert’s 12th problem in the particular case of imaginary quadratic fields. This particular case consists in giving explicit generators of the maximal abelian extension of an imaginary quadratic field. To deal with abelian extensions of such fields, we study the classical formulation of Class Field Theory and present the main statements without proofs. The other important ingredient for the proof we will describe is the theory of elliptic curves with complex multiplication. We will combine Class Field Theory with the notions of elliptic curves to prove the desired construction.
dc.format 96 p.
dc.format application/pdf
dc.language eng
dc.rights cc-by-nc-nd (c) Daniel Gil Muñoz, 2017
dc.rights http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights info:eu-repo/semantics/openAccess
dc.source Màster Oficial - Matemàtica Avançada
dc.subject Corbes el·líptiques
dc.subject Teoria de cossos de classe
dc.subject Treballs de fi de màster
dc.subject Extensions abelianes
dc.subject Teoria de torsió (Àlgebra)
dc.subject Geometria algebraica aritmètica
dc.subject Varietats abelianes
dc.subject Elliptic curves
dc.subject Class field theory
dc.subject Master's theses
dc.subject Abelian extensions
dc.subject Torsion theory (Algebra)
dc.subject Arithmetical algebraic geometry
dc.subject Abelian varieties
dc.title Explicit class field theory via elliptic curves
dc.type info:eu-repo/semantics/masterThesis


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