Curves of fixed gonality with many rational points

被引：0

作者：

Vermeulen, Floris ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B, B-3001 Leuven, Belgium

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2023年 / 35卷 / 01期

关键词：

EVERY GENUS;

D O I：

10.5802/jtnb.1240

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given an integer ? = 2 and an odd prime power q we show that for every large genus g there exists a non-singular curve C defined over F-q of genus g and gonality 7 and with exactly ?(q+1) F-q-rational points. This is the maximal number of rational points possible. This answers a recent conjecture by Faber-Grantham. Our methods are based on curves on toric surfaces and Poonen's work on squarefree values of polynomials.

引用

页码：135 / 149

页数：16

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