| Full text | |
| Author(s): |
Bootsma, Sven
;
Tafazolian, Saeed
;
Top, Jaap
Total Authors: 3
|
| Document type: | Journal article |
| Source: | FINITE FIELDS AND THEIR APPLICATIONS; v. 91, p. 13-pg., 2023-10-01. |
| Abstract | |
We study elliptic surfaces corresponding to an equation of the specific type y2 = x3 + f (t)x, defined over the finite field Fq for a prime power q -3 mod 4. It is shown that if s4 = f(t) defines a curve that is maximal over Fq2 then the rank of the group of sections defined over Fq on the elliptic surface is determined in terms of elementary properties of the rational function f(t). Similar results are shown for elliptic surfaces given by y2 = x3 + g(t) using prime powers q -5 mod 6 and curves s6 = g(t). Finally, for each of the forms used here, existence of curves with the property that they are maximal over Fq2 is discussed, as well as various examples.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/). (AU) | |
| FAPESP's process: | 22/06589-5 - Algebraic curves in positive characteristic |
| Grantee: | Saeed Tafazolian |
| Support Opportunities: | Regular Research Grants |