Geodesic
Visibility of the Shafarevich-Tate group at higher level
Documenta mathematica, Tome 12 (2007), pp. 673-696.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study visibility of Shafarevich--Tate groups of modular abelian varieties in Jacobians of modular curves of higher level. We prove a theorem about the existence of visible elements at a specific higher level under certain hypothesis which can be verified explicitly. We also provide a table of examples of visible subgroups at higher level and state a conjecture inspired by our data.
Classification : 11G05, 11G10, 11G18, 11Y40
Keywords: elliptic curves, abelian varieties, Mordell-Weil groups, Shafarevich-Tate groups, visibility 
@article{DOCMA_2007__12__a0,
     author = {Jetchev, Dimitar P. and Stein, William A.},
     title = {Visibility of the {Shafarevich-Tate} group at higher level},
     journal = {Documenta mathematica},
     pages = {673--696},
     publisher = {mathdoc},
     volume = {12},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2007__12__a0/}
}
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Jetchev, Dimitar P.; Stein, William A. Visibility of the Shafarevich-Tate group at higher level. Documenta mathematica, Tome 12 (2007), pp. 673-696. http://geodesic.mathdoc.fr/item/DOCMA_2007__12__a0/