Galois Representation on Elliptic Curve

dc.contributor.advisorBergeron, Nantel
dc.contributor.authorMin, Hyeck Ki
dc.date.accessioned2022-12-14T16:30:49Z
dc.date.available2022-12-14T16:30:49Z
dc.date.copyright2022-08-08
dc.date.issued2022-12-14
dc.date.updated2022-12-14T16:30:49Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelMaster's
dc.degree.nameMA - Master of Arts
dc.description.abstractThis thesis explores the orders of Galois representations about torsion subgroups of elliptic curves. We review the literature on elliptic curves and Serre's theorem. We describe a field formed by adjoining torsion subgroup of an elliptic curve. We show that the extension is finite and algebraic. Next, we construct a Galois group from the extension and use the relationship with a generalized linear group to find the possible values of the order of the Galois group. The order depends on the field where an elliptic curve is defined, the reducibility of f(x), and structure of the torsion subgroup. This approach provides the same insight as Serre's theorem that provides an upper bound of the order of Galois representation of an extended field given by adjoining a subgroup of points of an elliptic curve.
dc.identifier.urihttp://hdl.handle.net/10315/40693
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectMathematics
dc.subject.keywordsGalois representation
dc.subject.keywordsElliptic curves
dc.subject.keywordsGeneralized linear groups
dc.titleGalois Representation on Elliptic Curve
dc.typeElectronic Thesis or Dissertation

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