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June 2016 Finiteness of the Moderate Rational Points of Once-punctured Elliptic Curves
Yuichiro HOSHI
Hokkaido Math. J. 45(2): 271-291 (June 2016). DOI: 10.14492/hokmj/1470139405


In the present paper, we prove the {\it finiteness} of the set of {\it moderate} rational points of a once-punctured elliptic curve over a number field. This {\it finiteness} may be regarded as an analogue for a once-punctured elliptic curve of the well-known {\it finiteness} of the set of torsion rational points of an abelian variety over a number field. In order to obtain the {\it finiteness}, we discuss the {\it center} of the image of the pro-$l$ outer Galois action associated to a hyperbolic curve. In particular, we give, under the assumption that $l$ is {\it odd}, a {\it necessary and sufficient condition} for a certain hyperbolic curve over a generalized sub-$l$-adic field to have {\it trivial center}.


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Yuichiro HOSHI. "Finiteness of the Moderate Rational Points of Once-punctured Elliptic Curves." Hokkaido Math. J. 45 (2) 271 - 291, June 2016.


Published: June 2016
First available in Project Euclid: 2 August 2016

zbMATH: 06598415
MathSciNet: MR3532133
Digital Object Identifier: 10.14492/hokmj/1470139405

Primary: 14H30

Rights: Copyright © 2016 Hokkaido University, Department of Mathematics


Vol.45 • No. 2 • June 2016
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