The prime divisors in every class contain arbitrary large truncated classes

TL;DR

This paper proves that prime divisors in each class on a projective curve over a finite field include arbitrarily large truncated classes of effective divisors, revealing a rich structure of divisor classes.

Contribution

It establishes the existence of arbitrarily large truncated classes of effective divisors within prime divisors in each class on a projective curve over a finite field.

Findings

Prime divisors in each class contain arbitrarily large truncated classes.

The result applies to projective curves over finite fields.

Shows a deep structural property of divisor classes.

Abstract

We show that the prime divisors in every class on a projective curve over a finite field contain arbitrary large truncated generalized classes of finite effective divisors.