Curves on Frobenius classical surfaces in ℙ³ over finite fields

2021/11/18 by Elena Berardini, Jade Nardi, Berardini, Elena +1
Computer Science · Mathematics · #11G20 #14G05 #14H50 #14J70 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.09578

openalex publication_date 2021/11/18 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper we give an upper bound on the number of rational points on an irreducible curve C of degree δ defined over a finite field \mathbbF_q lying on a Frobenius classical surface S embedded in ℙ³. This leads us to investigate arithmetic properties of curves lying on surfaces. In a certain range of δ and q, our result improves all other known bounds in the context of space curves.

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