Explicit and quantitative results for abelian varieties over finite fields
| dc.contributor.author | Krause, Elliot, author | |
| dc.contributor.author | Achter, Jeffrey, advisor | |
| dc.contributor.author | Pries, Rachel, committee member | |
| dc.contributor.author | Juul, Jamie, committee member | |
| dc.contributor.author | Ray, Indrajit, committee member | |
| dc.date.accessioned | 2023-01-21T01:25:09Z | |
| dc.date.available | 2023-01-21T01:25:09Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | Let E be an ordinary elliptic curve over a prime field Fp. Attached to E is the characteristic polynomial of the Frobenius endomorphism, T2 − a1T + p, which controls several of the invariants of E, such as the point count and the size of the isogeny class. As we base change E over extensions Fpn, we may study the distribution of point counts for both of these invariants. Additionally, we look to quantify the rate at which these distributions converge to the expected distribution. More generally, one may consider these same questions for collections of ordinary elliptic curves and abelian varieties. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Krause_colostate_0053A_17519.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/236044 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2020- | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject | elliptic curve | |
| dc.subject | abelian varieties | |
| dc.title | Explicit and quantitative results for abelian varieties over finite fields | |
| dc.type | Text | |
| dc.type | Image | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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