{"paper":{"title":"Locally divergent orbits of maximal tori and values of forms at integral points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2015-02-08T20:25:04Z","abstract_excerpt":"Let $\\G$ be a semisimple algebraic group defined over a number field $K$, $\\te$ a maximal $K$-split torus of $\\G$, $\\mathcal{S}$ a finite set of valuations of $K$ containing the archimedean ones, $\\OO$ the ring of $\\mathcal{S}$-integers of $K$ and $K_\\mathcal{S}$ the direct product of the completions $K_v, v \\in \\mathcal{S}$. Denote $G = \\G(K_\\mathcal{S})$, $T = \\te(K_\\mathcal{S})$ and $\\Gamma = \\G(\\OO)$. Let $T\\pi(g)$ be a locally divergent orbit for the action of $T$ on $G/\\Gamma$ by left translations. We prove: ($1$) if $\\# S = 2$ then the closure $\\overline{T\\pi(g)}$ is a union of finitely"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02297","kind":"arxiv","version":5},"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"}