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.

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References in corpus (2)

• Locally trivial torsors that are not Weil-Châtelet divisible
• Vanishing of some Galois cohomology groups for elliptic curves

Cited by in corpus (1)

• Selmer groups are intersection of two direct summands of the adelic cohomology