I will outline what we know about the parity of ranks of elliptic curves and abelian varietes, and show some arithmetic phenomena that are predicted by this study. All existing theoretical results on the topic are conjectural: the unconditional statements concern either root numbers ("parity of the analytic rank") or dimensions of Selmer groups. At the end I will briefly sketch the proof of the parity conjecture for semistable abelian surfaces, that is that the Birch-Swinnerton-Dyer conjecture correctly predicts the parity of their ranks, assuming finiteness of the Tate-Shafarevich group and the functional equation. The latter is joint work with Celine Maistret.
Freitag, den 13. Januar 2017 um 13:30 Uhr, in INF205, SR C Freitag, den 13. Januar 2017 at 13:30, in INF205, SR C
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Gebhard Böckle