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

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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.
DOI : 10.4171/dm/238
Classification : 11G05, 11G10, 11G18, 11Y40
Mots-clés : abelian varieties, elliptic curves, Mordell-Weil groups, Shafarevich-Tate groups, visibility 
Dimitar P. Jetchev; William A. Stein. Visibility of the Shafarevich-Tate group at higher level. Documenta mathematica, Tome 12 (2007), pp. 673-696. doi: 10.4171/dm/238
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     author = {Dimitar P. Jetchev and William A. Stein},
     title = {Visibility of the {Shafarevich-Tate} group at higher level},
     journal = {Documenta mathematica},
     pages = {673--696},
     year = {2007},
     volume = {12},
     doi = {10.4171/dm/238},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/238/}
}
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