Rational points and Galois points for a plane curve over a finite field

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• 作者：Satoru Fukasawa¹ ; ^{s.fukasawa@sci.kj.yamagata-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 14H50 ; secondary ; 12F10 ; 14G05
• 刊名：Finite Fields and Their Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：39
• 期：Complete
• 页码：36-42
• 全文大小：253 K

文摘

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.