Torsion subgroups of elliptic curves over algebraic field extensions of Q

Trip, Manoy (2018) Torsion subgroups of elliptic curves over algebraic field extensions of Q. Bachelor's Thesis, Mathematics.

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Abstract

In this thesis, an overview of research in the field of torsion subgroups of elliptic curves over algebraic field extensions of Q is provided. This field of research is currently very active. In 2018, a result was published by Daniels et al. showing that the torsion subgroup of an elliptic curve is finite, when the underlying field is a Galois extension of Q and contains only finitely many roots of unity. The proof of this result is discussed in this report. Furthermore, the compositum of all prime degree extensions is treated. For this field extension, a sufficient criterion is provided for which the prime torsion of an elliptic curve over this field is trivial.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Derickx, M. and Top, J.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	01 Aug 2018
Last Modified:	08 Sep 2023 07:12
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/18190

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