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Cohomología de Galois y el Problema de Inmersión
(2022-06-02)
This text is the required master thesis that the author needs to present in order to obtain his Master’s degree in mathematics. It introduces the Galois embedding problem, focusing in Brauer type embedding problems, which ...
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Spaces of modular forms. Modular curves and dimensions
(2019-06-20)
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 ...
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The Néron-Ogg-Shafarevich Criterion for elliptic curves
(2020-09-07)
This text is the required master thesis that the author needs to present in order to obtain his Master’s degree in mathematics. It presents a proof of the Néron-Ogg-Shafarevich Criterion for elliptic curves over complete, ...
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Representaciones de Galois asociadas a curvas elípticas
(2023)
J.P Serre made, in his article ’Proprietes galoisiénnés des points d’ordre fini des courbes elliptiques’ published in 1972 [9], an study about the image of Galois representations attached to the 𝑙-torsion points of ...