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

### Brendan Creutz

#### Abstract

For every prime power $$p^n$$ with $$p = 2$$ or 3 and $$n > 1$$ 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 $$n$$. For these same prime powers we construct examples showing that the analogous local-global principle for divisibility in the Weil-Châtelet group can also fail.

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 Friday, May 24, 2013