{"paper":{"title":"The projective dimension of profinite modules for pro-p groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Thomas Weigel","submitted_at":"2013-03-23T18:06:02Z","abstract_excerpt":"The homology groups introduced by A. Brumer can be used to establish a criterion ensuring that a profinite $\\mathbb{F}_p[[G]]$-module of a pro-$p$ group $G$ has projective dimension $d<\\infty$ (cf. Thm. A). This criterion yields a new characterization of free pro-$p$ groups (cf. Cor. B). Applied to a semi-direct factor $G\\to\\mathbb{Z}_p\\to G$ isomorphic to $\\mathbb{Z}_p$ which defines a non-trivial end in the sense of A.A. Korenev one concludes that the closure of the normal closure of the image of $\\sigma$ is a free pro-$p$ subgroup (cf. Thm. C). From this result we will deduce a structure th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5872","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"}