Mathematical Research Letters

Volume 23 (2016)

Number 2

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

Pages: 377 – 387

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n2.a4

Author

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

Abstract

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.

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Published 6 June 2016