Open Access
March 2015 Linear relations and arithmetic on abelian schemes
Piotr Rzonsowski
Funct. Approx. Comment. Math. 52(1): 83-107 (March 2015). DOI: 10.7169/facm/2015.52.1.7


We investigate linear relations in Mordell-Weil groups of abelian varieties over finitely generated fields over $\mathbb{Q}$. Based on important and classical results for abelian varieties over these fields and on lifts of abelian varieties to suitable abelian schemes, we prove theorems concerning the reduction maps on torsion and non-torsion elements in Mordell-Weil groups of these varieties. These theorems and the arithmetic of abelian schemes and their endomorphism algebras are our key tools in the solutions of linear relation problems we work with in the last chapter of this paper.


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Piotr Rzonsowski. "Linear relations and arithmetic on abelian schemes." Funct. Approx. Comment. Math. 52 (1) 83 - 107, March 2015.


Published: March 2015
First available in Project Euclid: 20 March 2015

zbMATH: 06425015
MathSciNet: MR3326126
Digital Object Identifier: 10.7169/facm/2015.52.1.7

Primary: 11G10
Secondary: 14G05 , 14KXX , 14L15

Keywords: abelian scheme , abelian variety , Mordell-Weil group , support problem

Rights: Copyright © 2015 Adam Mickiewicz University

Vol.52 • No. 1 • March 2015
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