{"paper":{"title":"Quandles associated to Galois covers of arithmetic schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.NT","authors_text":"Nobuyoshi Takahashi","submitted_at":"2015-08-17T06:56:44Z","abstract_excerpt":"Let $X$ be a normal, separated and integral scheme of finite type over $\\mathbb{Z}$ and $\\mathcal{M}$ a set of closed points of $X$. To a Galois cover $\\tilde{X}$ of $X$ unramified over $\\mathcal{M}$, we associate a quandle whose underlying set consists of points of $\\tilde{X}$ lying over $\\mathcal{M}$. As the limit of such quandles over all \\'etale Galois covers and all \\'etale abelian covers, we define topological quandles $Q(X, \\mathcal{M})$ and $Q^\\mathrm{ab}(X, \\mathcal{M})$, respectively.\n  Then we study the problem of reconstruction. Let $K$ be $\\mathbb{Q}$ or a quadratic field, $\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03937","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"}