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On invisible elements of the Tate-Shafarevich group

✍ Scribed by Amod Agashé

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
475 KB
Volume
328
Category
Article
ISSN
0764-4442

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✦ Synopsis

Mazur [7]

has introduced the concept of visible elements in the Tate-Shafarevich group of optimal modular elliptic curves. We generalized the notion to arbitrary abelian subvarieties of abelian varieties and found, based on calculations that assume the Birch-Swinnerton-Dyer conjecture, that there are elements of the Tate-Shafarevich group of certain sub-abelian varieties of J,,(p) and .I, (p) that are not visible. 0 Academic des Sciences/Elsevier, Paris SW les &ments invisibles du groupe de Tate-Shafarevich R&urn& Muzur u introduit le concept d'e'lkments visibles du groupe de Tute-Shafurevich des courbes elliptiyues modulaires optimales. Nous avons g&+zlise' ce concept aux ,sousvarie'te's abe'liennes quelconques des varie'tPs abe'liennes, et trouvk, g&e ci des culculs reposant sur lu conjecture de Birch-Swinnerton-Dyer, qu 'il Y avait des e'l&lents du groupe de Tare-Shafarevich pour certaines sous-vnrie'te's abkennes de .J,, (1~) et .J, (11) qui ne sont pus visibles. 0 Academic des Sciences/Elsevier, Paris

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