Rational points on algebraic curves that change genus

[摘要] Let K be an algebraic function field in one variable over an algebraically closed field of positive characteristic p. We give an explicit upper bound for the number of rational points of genus-changing curves over K defined by y(p) = r(x) and show that every genus-changing curve of absolute genus 0 has finitely many K-rational points. We thus prove that every algebraic curve over K that admits genus change under base-field extensions has finitely many K-rational points. (C) 1997 Academic Press.

[发布日期] 1997-12-01