## Doctoral Dissertations

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

#### Author ORCID Identifier

https://orcid.org/0000-0003-4922-7831

#### Document Type

Open Access Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

2019

September

Siman Wong

Number Theory

#### Abstract

In this thesis, we prove that, a selfdual 3-dimensional Galois representation constructed by van Geemen and Top is isomorphic to a quadratic twist of the symmetric square of the Tate module of an elliptic curve. This is an application of our refinement of the Faltings-Serre method to 3-dimensional Galois representations with ground field not equal to Q. The proof makes use of the Faltings-Serre method, $\ell$-adic Lie algebra, and Burnside groups.

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