Bootsma, Sven (2023) On Certain Elliptic Surfaces With j-Invariant Zero Over Prime Fields of Positive Characteristic. Master's Thesis / Essay, Mathematics.
|
Text
mMATH_2023_BootsmaSE.pdf Download (889kB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
toestemming.pdf Restricted to Registered users only Download (128kB) |
Abstract
We find prime numbers p so that the elliptic surface defined by the equation y^2 = x^3 + t^360 + 1 has Mordell-Weil rank 68 over F_p. Moreover, we show that, up to finite index, these generating sections are obtained from a reduction modulo p of the characteristic zero case. Furthermore, using both the Tate conjecture for abelian varieties over finite fields and the theory of F_{q^2} -maximal curves, where q is a prime power, we prove that the family of elliptic surfaces over F_p defined by the equation y^2 = x^3 + t^(p+1) + 1 has Mordell-Weil rank p − 1.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Top, J. and Salgado Guimaraes da Silva, C. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 01 Feb 2023 09:46 |
| Last Modified: | 01 Feb 2023 09:46 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/29188 |
Actions (login required)
 |
View Item |