Locally trivial torsors that are not Weil-Châtelet divisible

Abstract

For every prime p we give infinitely many examples of torsors under abelian varieties over Q that are locally trivial but not divisible by p in the Weil-Châtelet group. We also give an example of a locally trivial torsor under an elliptic curve over Q which is not divisible by 4 in the Weil-Châtelet group. This gives a negative answer to a question of Cassels.

v2: updated/corrected bibliography

Cited by in corpus (3)

• Two torsion in the Brauer group of a hyperelliptic curve
• Local-global principles for Weil-Châtelet divisibility in positive characteristic
• Local-global divisibility on algebraic tori