{"paper":{"title":"Towers of torsors over a field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Marco Antei, Michel Emsalem","submitted_at":"2016-06-28T12:21:06Z","abstract_excerpt":"Let $X$ be a projective, connected and smooth scheme defined over an algebraically closed field $k$. In this paper we prove that a tower of finite torsors (i.e., under the action of finite $k$-group schemes) can be dominated by a single finite torsor. Let $G$ be any finite $k$-group scheme and $Y$ any $G$--torsor over $X$ pointed in $y\\,\\in\\, Y(k)$; we define over $Y$, which may not be reduced, in a very natural way the categories of Nori-semistable and essentially finite vector bundles. These categories are proved to be Tannakian. Their Galois $k$-group schemes $\\pi^S(Y,\\,y)$ and $\\pi^N(Y,\\,y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08671","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"}