On the number of rational points on Prym varieties over finite fields

MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM

We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

The Minimum and Maximum Number of Rational Points on Jacobian Surfaces over Finite Fields

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 dimension 2.

On the Number of Rational Points on Drinfeld Modular Varieties over Finite Fields

Drinfeld and Vladut proved that Drinfeld modular curves have many Fq2 -rational points compared to their genera. We propose a conjectural generalization of this result to higher dimensional Drinfeld modular varieties, and prove a theorem giving some evidence for the conjecture.

The Number of Rational Points on DrinfeldModular Varieties over Finite Fields

Mirror Congruence For Rational Points On Calabi-Yau Varieties

One of the basic problems in arithmetic mirror symmetry is to compare the number of rational points on a mirror pair of Calabi-Yau varieties. At present, no general algebraic geometric definition is known for a mirror pair. But an important class of mirror pairs comes from certain quotient construction. In this paper, we study the congruence relation for the number of rational points on a quoti...