Javascript must be enabled for the correct page display

Finite groups of automorphisms on genus one curves without rational points

Roelfszema, Majken (2018) Finite groups of automorphisms on genus one curves without rational points. Master's Thesis / Essay, Mathematics.

[img]
Preview
Text
mMATH_2018_RoelfszemaMT.pdf

Download (1MB) | Preview
[img] Text
toestemming.pdf
Restricted to Registered users only

Download (135kB)

Abstract

Mazur’s theorem concerning rational torsion points on elliptic curves over Q (the rationals) can be reformulated as follows. Given is a genus one curve X over Q. Let σ and τ be involutions in the automorphism group over Q of X, Aut(X), and suppose the group G ⊂ Aut(X) generated by σ and τ is finite. Then G is a dihedral group of order 2n, with n ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}. Examples where X = E is an elliptic curve over Q are relatively easy to construct. The aim of this thesis is for each possible n to find curves X where X(Q) = ∅. In order to visualize the situation, the context of Poncelet figures is used. A Poncelet figure containing an n-gon can be made using X exactly when Aut(X) has such a subgroup G of order 2n.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor:
Supervisor nameSupervisor E mail
Top, J.J.Top@rug.nl
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 13 Jul 2018
Last Modified: 20 Jul 2018 12:25
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/17862

Actions (login required)

View Item View Item