Related papers: Number of points on abelian and Jacobian varieties…

We give some bounds on the numbers of rational points on abelian varieties and jacobians varieties over finite fields. The main result is that we determine the maximum and minimum number of rational points on jacobians varieties of…

We study the distribution of algebraic points on curves in abelian varieties over finite fields.

We establish some upper and lower bounds for the number of rational points of Prym varieties over finite fields.

We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.

We compute the number of points over finite fields of some algebraic varieties related to cluster algebras of finite type. More precisely, these varieties are the fibers of the projection map from the cluster variety to the affine space of…

This paper is concerned with some Algebraic Geometry codes on Jacobians of genus 2 curves. We derive a lower bound for the minimum distance of these codes from an upper "Weil type" bound for the number of rational points on irreducible…

We provide in this paper an upper bound for the number of rational points on a curve defined over a one variable function field over a finite field. The bound only depends on the curve and the field, but not on the Jacobian variety of the…

In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in…

In this paper we establish a new lattice description for superspecial abelian varieties over a finite field $\mathbb {F}_q$ of $q=p^a$ elements. Our description depends on the parity of the exponent $a$ of $q$. When $q$ is an odd power of…

This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers, the current authors and T.-C. Yang obtain explicit formulas for the numbers of superspecial abelian surfaces over…

We investigate the large values of class numbers of cubic fields, showing that one can find arbitrary long sequences of "close" abelian cubic number fields with class numbers as large as possible. We also give a first step toward an…

In this note, we propose the modular height of an abelian variety defined over a field of finite type over Q. Moreover, we prove its finiteness property.

In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.

We give a bound on the number of points of order two on the theta divisor of a principally polarized abelian variety A. When A is the Jacobian of a curve C the result can be applied in estimating the number of effective square roots of a…

We give an upper bound for the number of points of a hypersurface over a finite field that has no lines on, in terms of the dimension, the degree, and the number of the elements of the finite field.

We compute the exact values of the Jordan constants of abelian surfaces over finite fields.

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

We give an upper bound on the number of rational points of an arbitrary Zariski closed subset of a projective space over a finite field. This bound depends only on the dimensions and degrees of the irreducible components and holds for very…

In this paper we provide an algorithm to classify groups of points on abelian threefolds over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $\mathbb{F}_q$-isogeny class. This work…

In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…