Rational points and Galois points for a plane curve over a finite field
Rational points and Galois points for a plane curve over a finite field
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有限域上平面曲线的有理点和伽罗瓦点
DOI：
10.1016/j.ffa.2016.01.003
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发表时间：
2016
影响因子：
1
通讯作者：
Satoru Fukasawa
中科院分区：
文献类型：
--
作者：
Satoru Fukasawa;Kei Miura;Isamu Iwanari;薩摩 順吉，友枝 明保;Satoru Fukasawa
研究了有限域上平面曲线的有理点与伽罗瓦点之间的关系。如果曲线是Hermitian曲线、Klein四次曲线或Ballico-Hefez曲线，则Galois点的集合与射影平面上有理点的集合重合。作者提出了一个问题：反之成立吗？如果亏格0或1的曲线有一个有理点，我们就有一个肯定的答案。
We study the relationship between rational points and Galois points for a plane curve over a finite field. It is known that the set of Galois points coincides with that of rational points of the projective plane if the curve is the Hermitian, Klein quartic or Ballico–Hefez curve. The author proposes a problem:Does the converse hold true?If the curve of genus zero or one has a rational point, we have an affirmative answer.