Functiones et Approximatio Commentarii Mathematici

Hasse principle for linear dependence in Mordell-Weil groups

Stefan Barańczuk

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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.

Article information

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

Dates
First available in Project Euclid: 26 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.facm/1572055503

Digital Object Identifier
doi:10.7169/facm/1792

Mathematical Reviews number (MathSciNet)
MR4074388

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

Keywords
Mordell-Weil groups rank linear dependence local-global principle

Citation

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. https://projecteuclid.org/euclid.facm/1572055503


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References

  • [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.