Show your Sha Nils Bruin I'll try and give a gentle introduction to explicit "visualisation constructions" for Schafarevich-Tate groups of Jacobians of Hyperelliptic curves and elliptic curves. The idea is to embed an abelian variety J in a higher dimensional one. By comparing selmer groups, one can hope one can conclude something about the Shafarevich-Tate groups. In practice these methods work quite well.