JournalscmhVol. 88, No. 2pp. 323–352

Detecting linear dependence on an abelian variety via reduction maps

  • Peter Jossen

    Université Paris-Sud, Orsay, France
Detecting linear dependence on an abelian variety via  reduction maps cover

Abstract

Let AA be a geometrically simple abelian variety over a number field kk, let XX be a subgroup of A(k)A(k) and let PA(k)P\in A(k) be a rational point. We prove that if PP belongs to XX modulo almost all primes of kk then PP already belongs to XX.

Cite this article

Peter Jossen, Detecting linear dependence on an abelian variety via reduction maps. Comment. Math. Helv. 88 (2013), no. 2, pp. 323–352

DOI 10.4171/CMH/287