Weil–Châtelet divisible elements in Tate–Shafarevich groups I: The Bashmakov problem for elliptic curves over $ \mathbb{Q} $

Publisher： Cambridge University Press

E-ISSN： 1570-5846|149|5|729-753

ISSN： 0010-437x

Source： Compositio Mathematica, Vol.149, Iss.5, 2013-05, pp. : 729-753

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Abstract

For an abelian variety $A$ over a number field $k$ we discuss the maximal divisible subgroup of ${\mathrm{H} }^{1} (k, A)$ and its intersection with the subgroup Ш $(A/ k)$ . The results are most complete for elliptic curves over $ \mathbb{Q} $ .

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