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

TL;DR

This paper establishes bounds and exact counts for the number of rational points on Prym varieties over finite fields, focusing on dimension 2 cases to enhance understanding of their point distributions.

Contribution

It provides new bounds and exact maximum and minimum counts for rational points on Prym varieties, especially in dimension 2, advancing knowledge in algebraic geometry over finite fields.

Findings

Derived upper and lower bounds for rational points on Prym varieties.

Determined exact maximum and minimum counts for dimension 2 Prym varieties.

Enhanced understanding of point distributions on Prym varieties over finite fields.

Abstract

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.