Functiones et Approximatio Commentarii Mathematici

Hasse principle for linear dependence in Mordell-Weil groups

Stefan Barańczuk

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Funct. Approx. Comment. Math., Volume 62, Number 1 (2020), 81-85.

First available in Project Euclid: 26 October 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]
Secondary: 11H52

Mordell-Weil groups rank linear dependence local-global principle


Barańczuk, Stefan. Hasse principle for linear dependence in Mordell-Weil groups. Funct. Approx. Comment. Math. 62 (2020), no. 1, 81--85. doi:10.7169/facm/1792.

Export citation


  • [1] S. Barańczuk, On a dynamical local-global principle in Mordell–Weil type groups, Expo. Math. 35 (2017), no. 2, 206–211.
  • [2] S. Barańczuk, On reduction maps and support problem in $K$-theory and abelian varieties, J. Number Theory 119 (2006), no. 1, 1–17.
  • [3] Y. Flicker, P. Krasoń, Multiplicative relations of points on algebraic groups, Bull. Pol. Acad. Sci. Math. 65 (2017), no. 2, 125–138.
  • [4] J.-P. Serre, A course in Arithmetic, Graduate Texts in Mathematics, Springer 1996.
  • [5] J.H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, Volume 106, 2009.