The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Commentarii Mathematici Helvetici


Full-Text PDF (292 KB) | Metadata | Table of Contents | CMH summary
Volume 88, Issue 2, 2013, pp. 323–352
DOI: 10.4171/CMH/287

Published online: 2013-04-24

Detecting linear dependence on an abelian variety via reduction maps

Peter Jossen[1]

(1) Université Paris-Sud, Orsay, France

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

Keywords: Abelian varieties, local-global principles, Mordell–Weil group

Jossen Peter: Detecting linear dependence on an abelian variety via reduction maps. Comment. Math. Helv. 88 (2013), 323-352. doi: 10.4171/CMH/287