Tate-Shafarevich groups and K3 surfaces

Abstract

Following (and elaborating on) a method of Logan and van Luijk, we exhibit explicit genus-2 curves whose Jacobians have nontrivial 2-torsion in their Tate-Shafarevich groups.

17 pages, comments welcome

References in corpus (2)

• The Cassels-Tate pairing on polarized abelian varieties
• Nontrivial elements of Sha explained through K3 surfaces