{"paper":{"title":"The Heisenberg coboundary equation: appendix to Explicit Chabauty-Kim theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ishai Dan-Cohen, Stefan Wewers","submitted_at":"2014-03-18T11:35:47Z","abstract_excerpt":"Let p be a regular prime number, let Gp denote the Galois group of the maximal unramified away from p extension of Q, and let H_et denote the Heisenberg group over Qp with Gp-action given by H_et = Qp(1)^2 \\oplus Qp(2). Although Soul\\'e vanishing guarantees that the map H^1(Gp, H_et) ---> H^1(Gp, Qp(1)^2) is bijective, the problem of constructing an explicit lifting of an arbitrary cocycle in H^1(Gp, Qp(1)^2) proves to be a challenge. We explain how we believe this problem should be analyzed, following an unpublished note by Romyar Sharifi, hereby making the original appendix to Explicit Chaba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4414","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"}