UBC Number Theory Seminar: Nils Bruin

A classical method for exhibiting non-trivial elements in the Tate-Shafarevich group of Jacobians compares Selmer groups of various isogenies. In this presentation we consider Jacobians of plane quartics that have a (2,2,2)-isogeny to another principally polarized abelian variety. An interesting complication is that such an abelian variety may not be a Jacobian: it may only be a quadratic twist of a Jacobian. We describe how, at least in the case of completely split 2-torsion, one can determine which quadratic twist and how one can still compute Selmer groups. This talk describes joint work with Damara Gagnier and with Emiel Haakma.