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March 2020 Hasse principle for linear dependence in Mordell-Weil groups
Stefan Barańczuk
Funct. Approx. Comment. Math. 62(1): 81-85 (March 2020). DOI: 10.7169/facm/1792

Abstract

We establish a local-global principle for linear dependence of points in Mordell--Weil groups of abelian varieties over number fields. We give a complete characterization, in terms of a relation between the rank and the dimension, of abelian varieties with endomorphism ring equal to $\mathbb{Z}$ for which the principle holds. In the case of elliptic curves we prove the result in full generality, i.e., without the assumption on the endomorphism ring.

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Stefan Barańczuk. "Hasse principle for linear dependence in Mordell-Weil groups." Funct. Approx. Comment. Math. 62 (1) 81 - 85, March 2020. https://doi.org/10.7169/facm/1792

Information

Published: March 2020
First available in Project Euclid: 26 October 2019

zbMATH: 07225500
MathSciNet: MR4074388
Digital Object Identifier: 10.7169/facm/1792

Subjects:
Primary: 11G10
Secondary: 11H52

Rights: Copyright © 2020 Adam Mickiewicz University

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Vol.62 • No. 1 • March 2020
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