Explicit class field theory via elliptic curves
| Autor: | Gil Muñoz, Daniel |
|---|---|
| Přispěvatelé: | Guitart Morales, Xavier |
| Rok vydání: | 2017 |
| Předmět: |
Master's theses
Corbes el·líptiques Class field theory Master's thesis Treballs de fi de màster Extensions abelianes Torsion theory (Algebra) Varietats abelianes Teoria de torsió (Àlgebra) Abelian varieties Abelian extensions Teoria de cossos de classe Geometria algebraica aritmètica Elliptic curves Arithmetical algebraic geometry |
| Zdroj: | Dipòsit Digital de la UB Universidad de Barcelona |
| Popis: | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Xavier Guitart Morales [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. |
| Databáze: | OpenAIRE |
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