Calculations for the etale fundamental group of curves of genus one or two
| dc.contributor.advisor | Ramachandran, Niranjan | en_US |
| dc.contributor.author | Lizzi, Adam Joseph | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2018-09-07T05:32:56Z | |
| dc.date.available | 2018-09-07T05:32:56Z | |
| dc.date.issued | 2018 | en_US |
| dc.description.abstract | The \'etale fundamental group $\pi_{1, \text{\'et}}(C)$ is a profinite group which classifies covers of algebraic-geometric objects. Its abelianizaton classifies torsors over $C$ with a finite, abelian structure group. When $C$ is a curve over a number field $K$, $\pi_{1, \text{\'et}}^{\textsf{ab}}(C)$ possesses a finite subgroup $\Ker(C/K)$ which records which abelian \'etale covers of $C$ come from geometry. In this thesis multiple algorithms for calculating $\Ker(E/K)$ are presented when $E$ is an elliptic curve over a number field. We indicate how to generalize one of these algorithms to the Jacobian of a genus two curve $C$, allowing for progress to be made on calculating $\Ker(C/K)$. | en_US |
| dc.identifier | https://doi.org/10.13016/M2TB0XZ7N | |
| dc.identifier.uri | http://hdl.handle.net/1903/21123 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | elliptic curves | en_US |
| dc.subject.pquncontrolled | etale fundamental group | en_US |
| dc.subject.pquncontrolled | jacobian | en_US |
| dc.subject.pquncontrolled | number theory | en_US |
| dc.title | Calculations for the etale fundamental group of curves of genus one or two | en_US |
| dc.type | Dissertation | en_US |
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