Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves

Computing zeta functions of Artin-Schreier curves over finite fields II

Polars of Artin–schreier Curves

1. Introduction. In this paper we study some properties of the special family of Artin–Schreier curves related to the theory of polar curves we developed in [2]. Our goal is to show how this theory can be carried out in concrete situations and also show how it can be used to determine new upper bounds for the number of rational points of projective plane curves over finite fields. The method we...

Newton Slopes for Artin-schreier-witt Towers

We fix a monic polynomial f(x) ∈ Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves · · · → Cm → Cm−1 → · · · → C0 = A, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tow...

Weil Descent Attack for Artin-Schreier Curves

In this paper, we show how the method introduced by Gaudry, Hess and Smart can be extended to a family of algebraic curves using Artin-Schreier extensions. This family also extends the number of hyperelliptic curves in characteristic 2 vulnarable to the Weil decent attack obtained by Galbraith. We also show that the genus of the resulting curve will be one of two easily computable values.

Some Families of Supersingular Artin - Schreier Curves

A curve over finite field is supersingular if its Jacobian is supersingular as an abelian variety. On the one hand, supersingular abelian varieties form the smallest (closed) stratum in the moduli space of abelian varieties, on the other the intersection of Jacobian locus and the stratification of moduli space is little known. Consequently it is very difficult to locate a family of supersingula...