Local-global principles for Weil–Châtelet divisibility in positive characteristic

Abstract We extend existing results characterizing Weil-Châtelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of González-Avilés and Tan, we characterize when local-global divisibility holds in such contexts, providing examples showing that these results are optimal. We give an example of an elliptic curve over a global field of characteristic 2 containing a rational point which is locally divisible by 8, but is not divisible by 8 as well as examples showing that the analogous local-global principle for divisibility in the Weil-Châtelet group can also fail.