arXiv subjects
Publications and source records attributed to Gerard van der Geer.
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of class field theory.
The weight hierarchy of generalized Reed-Muller codes over arbitrary finite fields was determined by Heijnen and Pellikaan. In this paper we produce curves over finite fields with many points which are closely related to this weight hierarchy.
In this paper a number of results on cycles on the moduli space of principally polarized abelian varieties is presented. Results include a determination of the tautological ring, bounds on the order of torsion of the top Chern class $λ_g$ and a determination of the cycle classes of the Ekedahl-Oort stratification in characteristic $p$. It includes as special cases formulas for the classes of loci like the $p$-rank $\leq f$ locus or the $a$-number $\geq a$-locus. The results on the tautological ring are my own work, the results on the torsion of $λ_g$ and on the cycle classes of the Ekedahl-Oort stratification are joint work with Torsten Ekedahl and some of the results on curves are joint work with Carel Faber.
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.