Elliptic Curves over Finite Fields and their l-Torsion Galois Representations
dc.contributor.author | Baker, Michael | |
dc.date.accessioned | 2015-09-08 13:32:02 (GMT) | |
dc.date.available | 2015-09-08 13:32:02 (GMT) | |
dc.date.issued | 2015-09-08 | |
dc.date.submitted | 2015-08-25 | |
dc.identifier.uri | http://hdl.handle.net/10012/9649 | |
dc.description.abstract | 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 $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong \widehat{\mathbf Z}$ on its $\ell$-torsion subgroup $E[\ell]$. This leads us to the problem of counting elliptic curves with prescribed $\ell$-torsion Galois representations, which we answer for small primes $\ell$ by counting rational points on suitable modular curves. The resulting exact formulas yield expressions for certain sums of Hurwitz class numbers. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | |
dc.subject | elliptic curves | en |
dc.subject | modular forms | en |
dc.subject | Hurwitz class numbers | en |
dc.subject | quadratic forms | en |
dc.subject | modular curves | en |
dc.title | Elliptic Curves over Finite Fields and their l-Torsion Galois Representations | en |
dc.type | Master Thesis | en |
dc.pending | false | |
dc.subject.program | Pure Mathematics | en |
uws-etd.degree.department | Pure Mathematics | en |
uws-etd.degree | Master of Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |