{"paper":{"title":"Noether's problem and unramified Brauer groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Akinari Hoshi, Boris E. Kunyavskii, Ming-chang Kang","submitted_at":"2012-02-27T02:04:42Z","abstract_excerpt":"Let $k$ be any field, $G$ be a finite group acing on the rational function field $k(x_g:g\\in G)$ by $h\\cdot x_g=x_{hg}$ for any $h,g\\in G$. Define $k(G)=k(x_g:g\\in G)^G$. Noether's problem asks whether $k(G)$ is rational (= purely transcendental) over $k$. It is known that, if $\\bm{C}(G)$ is rational over $\\bm{C}$, then $B_0(G)=0$ where $B_0(G)$ is the unramified Brauer group of $\\bm{C}(G)$ over $\\bm{C}$. Bogomolov showed that, if $G$ is a $p$-group of order $p^5$, then $B_0(G)=0$. This result was disproved by Moravec for $p=3,5,7$ by computer calculations. We will prove the following theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5812","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"}