{"paper":{"title":"Abelian-by-Central Galois groups of fields I: a formal description","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adam Topaz","submitted_at":"2013-10-21T15:51:51Z","abstract_excerpt":"Let $K$ be a field whose characteristic is prime to a fixed integer $n$ with $\\mu_n \\subset K$, and choose $\\omega \\in \\mu_n$ a primitive $n$th root of unity. Denote the absolute Galois group of $K$ by $\\operatorname{Gal}(K)$, and the mod-$n$ central-descending series of $\\operatorname{Gal}(K)$ by $\\operatorname{Gal}(K)^{(i)}$. Recall that Kummer theory, together with our choice of $\\omega$, provides a functorial isomorphism between $\\operatorname{Gal}(K)/\\operatorname{Gal}(K)^{(2)}$ and $\\operatorname{Hom}(K^\\times,\\mathbb{Z}/n)$. Analogously to Kummer theory, in this note we use the Merkurje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5613","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"}