Mathematical Research Letters

Volume 23 (2016)

Number 2

On the local-global principle for divisibility in the cohomology of elliptic curves

Pages: 377 – 387



Brendan Creutz (School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand)


For every prime power $p^n$ with $p = 2$ or $3$ and $n \geq 2$ we give an example of an elliptic curve over $\mathbb{Q}$ containing a rational point which is locally divisible by $p^n$ but is not divisible by $p^n$. For these same prime powers we construct examples showing that the analogous local-global principle for divisibility in theWeil–Châtelet group can also fail.

Accepted 3 December 2015

Published 6 June 2016