{"paper":{"title":"Wild Kernels and divisibility in K-groups of global fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.NT","authors_text":"Grzegorz Banaszak","submitted_at":"2012-08-10T10:37:01Z","abstract_excerpt":"In this paper we study the divisibility and the wild kernels in algebraic K-theory of global fields $F.$ We extend the notion of the wild kernel to all K-groups of global fields and prove that Quillen-Lichtenbaum conjecture for $F$ is equivalent to the equality of wild kernels with corresponding groups of divisible elements in K-groups of $F.$ We show that there exist generalized Moore exact sequences for even K-groups of global fields. Without appealing to the Quillen-Lichtenbaum conjecture we show that the group of divisible elements is isomorphic to the corresponding group of \\' etale divis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2137","kind":"arxiv","version":1},"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"}