Back to matchesWe found a matchYour institution may have access to this item. Find your institution then sign in to continue.TitleWeil–Châtelet divisible elements in Tate–Shafarevich groups I: The Bashmakov problem for elliptic curves over $ \mathbb{Q} $.AuthorsÇiperiani, Mirela; Stix, JakobAbstractFor 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} $.SubjectsDIVISIBILITY groups; GROUP theory; ELLIPTIC curves; ABELIAN varieties; NUMBER theory; ALGEBRAIC field theoryPublicationCompositio Mathematica, 2013, Vol 149, Issue 5, p729ISSN0010-437XPublication typeArticleDOI10.1112/S0010437X12000747