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

2013/05/25 by Creutz, Brendan · 1 citation
#11G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1305.5881

Abstract

For every prime power pⁿ with p = 2 or 3 and n > 1 we give an example of an elliptic curve over Q containing a rational point which is locally divisible by pⁿ but is not divisible by pⁿ. 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.

Cited by

• On the Hasse principle for divisibility in elliptic curves

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