Fibre products of Kummer covers and curves with many points
Applicable Algebra in Engineering, Communications and Computing, vol.18, no.5, pp.433-443, 2007 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 18 Issue: 5
- Publication Date: 2007
- Doi Number: 10.1007/s00200-007-0047-8
- Journal Name: Applicable Algebra in Engineering, Communications and Computing
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.433-443
- Middle East Technical University Affiliated: Yes
Abstract
We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (http://www.science.uva.nl/(similar to)geer/tables-mathcomp15.ps).