Visualizing Elements of Shafarevich-Tate Groups at Higher Level

by Dimitar Jetchev and William Stein

Abstract

We consider visibility of Shafarevich-Tate groups of modular abelian varieties in modular Jacobians of higher level, and give hypotheses that imply the existence of visible elements at a specific higher level. We also give a table of elements that are visible at higher level, and make conjectures inspired by our results.



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