{"paper":{"title":"On a Localisation Sequence for the K-Theory of Skew Power Series Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RA"],"primary_cat":"math.KT","authors_text":"Malte Witte","submitted_at":"2011-09-15T18:53:01Z","abstract_excerpt":"Let $B=A[[t;\\sigma,\\delta]]$ be a skew power series ring such that $\\sigma$ is given by an inner automorphism of $B$. We show that a certain Waldhausen localisation sequence involving the K-theory of $B$ splits into short split exact sequences. In the case that $A$ is noetherian we show that this sequence is given by the localisation sequence for a left denominator set $S$ in $B$. If $B=Z_p[[G]]$ happens to be the Iwasawa algebra of a $p$-adic Lie group $G\\isomorph H\\rtimes Z_p$, this set $S$ is Venjakob's canonical Ore set. In particular, our result implies that\n  $$ 0--> K_{n+1}(Z_p[[G]])-->"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3423","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"}