An upper bound for the genus of a curve without points of small degree

2012/03/05 by Claudio Stirpe, Stirpe, Claudio
Computer Science · Mathematics · #11G45 #11R37 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1203.0945

openalex publication_date 2012/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper I prove that for any prime p there is a constant C_p>0 such that for any n>0 and for any p-power q there is a smooth, projective, absolutely irreducible curve over \mathbbF_q of genus g≤ C_p qⁿ without points of degree smaller than n.

Related

• Closed points on curves over finite fields
• The genus of curves in \mathbb P⁴ and \mathbb P⁵ not contained in quadrics
• On the genus of projective curves not contained in hypersurfaces of given degree, II
• A bound on the genus of a curve with Cartier operator of small rank
• Curves of every genus with many points, II: Asymptotically good families