{"paper":{"title":"Embedding functors and their arithmetic properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ting-Yu Lee","submitted_at":"2012-11-15T10:28:38Z","abstract_excerpt":"In this article, we focus on how to embed a torus $\\rT$ into a reductive group $\\rG$ with respect to a given root datum $\\Psi$ over a scheme $\\rS$. This problem also relates to how to embed an \\'etale algebra with involution into a central simple algebra with involution (cf. \\cite{PR1}). We approach this problem by defining the embedding functor, and prove that the embedding functor is representable and is a left homogeneous space over $\\rS$ under the automorphism group of $\\rG$. In order to fix a connected component of the embedding functor, we define an orientation $u$ of $\\Psi$ with respect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3564","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"}