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Invisibility of Tate-Shafarevich groups in abelian surfaces

We give some examples of elliptic curves over the rationals whose Tate-Shafarevich groups contain elements of order 6 or 7 that are not visible in an abelian surface. We then show that some of these elements are visible in an abelian threefold.

Invisibility of Tate-Shafarevich groups in abelian surfaces   (13 pages)     dvi   ps   ps.gz   pdf