Torsion Packet Envelope and Rational Points of Algebraic Curves
Ryo Ichikawa
TL;DR
This paper introduces a new elementary method utilizing torsion packets to determine rational points on algebraic curves, providing explicit examples where the entire set of rational points can be found.
Contribution
The paper presents a novel elementary approach for finding rational points on algebraic curves using torsion packets, with practical examples demonstrating its effectiveness.
Findings
Method successfully determines all rational points on certain curves.
Provides explicit examples illustrating the method's application.
Enhances understanding of rational points via torsion packet analysis.
Abstract
In this paper, we give an elementary new method for determining the rational points on algebraic curves using torsion packets. We also provide examples of curves for which all rational points can be completely determined by our method.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications