Hasse principle for Kummer varieties (joint work with Yonatan Harpaz)

4 December 2014
16:00
Alexei Skorobogatov
Abstract

Rational points on Kummer varieties can be studied through the variation of Selmer groups of quadratic twists of the underlying abelian variety, using an idea of Swinnerton-Dyer. We consider the case when the Galois action on 2-torsion has a large image. Under a mild additional assumption we prove the Hasse principle assuming the finiteness of relevant Shafarevich-Tate groups. This approach is inspired by the work of Mazur and Rubin.

  • Number Theory Seminar