{"paper":{"title":"Prime Decomposition and the Iwasawa mu-invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Maire, Farshid Hajir","submitted_at":"2016-01-16T18:35:12Z","abstract_excerpt":"For $\\Gamma=\\mathbb{Z}_p$, Iwasawa was the first to construct $\\Gamma$-extensions over number fields with arbitrarily large $\\mu$-invariants. In this work, we investigate other uniform pro-$p$ groups which are realizable as Galois groups of towers of number fields with arbitrarily large $\\mu$-invariant. For instance, we prove that this is the case if $p$ is a regular prime and $\\Gamma$ is a uniform pro-$p$ group admitting a fixed-point-free automorphism of odd order dividing $p-1$. Both in Iwasawa's work, and in the present one, the size of the $\\mu$-invariant appears to be intimately related "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04195","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"}