The period-index problem in WC-groups II: abelian varieties

Abstract

We study the relationship between the period and the index of a principal homogeneous space over an abelian variety, obtaining results which generalize work of Cassels and Lichtenbaum on curves of genus one. In addition, we show that the p-torsion in the Shafarevich-Tate group of a fixed abelian variety over a number field k grows arbitrarily large when considered over field extensions l/k of bounded degree. Essential use is made of an abelian variety version of O'Neil's period-index obstruction.

28 pages

References in corpus (1)

• The Cassels-Tate pairing on polarized abelian varieties

Cited by in corpus (6)

• Selmer groups and class groups
• Potential Sha for abelian varieties
• Quadratic points on intersections of two quadrics
• Curves over global fields violating the Hasse Principle
• The period-index problem in WC-groups I: elliptic curves
• The period-index problem for elliptic curves and the essential dimension of Picard stacks