{"paper":{"title":"Closures of locally divergent orbits of maximal tori and values of homogeneous forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2018-01-05T10:53:37Z","abstract_excerpt":"Let $\\G$ be a semisimple algebraic group over a number field $K$, $\\mathcal{S}$ a finite set of places of $K$, $K_\\mathcal{S}$ the direct product of the completions $K_v, v \\in \\mathcal{S}$, and $\\OO$ the ring of $\\mathcal{S}$-integers of $K$. Let $G = \\G(K_\\mathcal{S})$, $\\Gamma = \\G(\\OO)$ and $\\pi:G \\rightarrow G/\\Gamma$ the quotient map. We describe the closures of the locally divergent orbits ${T\\pi(g)}$ %in $G/\\Gamma$ where $T$ is a maximal $K_\\mathcal{S}$-split torus in $G$. If $\\# S = 2$ then the closure $\\overline{T\\pi(g)}$ is a finite union of $T$-orbits stratified in terms of parabol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02497","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"}