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• #### Elliptic Curves over Finite Fields and their l-Torsion Galois Representations ﻿

(University of Waterloo, 2015-09-08)
Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of \$\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ...
• #### Quaternion Algebras and Quadratic Forms ﻿

(University of Waterloo, 2008-05-12)
The main goal of this Masters' thesis is to explore isomorphism types of quaternion algebras using the theory of quadratic forms, number theory and algebra. I would also present ways to characterize quaternion algebras, ...

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