{"paper":{"title":"Local-global principles for Weil-Ch\\^atelet divisibility in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz, Jos\\'e Felipe Voloch","submitted_at":"2016-08-03T21:57:44Z","abstract_excerpt":"We extend existing results characterizing Weil-Ch\\^atelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of Gonz\\'alez-Avil\\'es 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01371","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}