{"paper":{"title":"Totally Ramified Maximal Tori and Bruhat-Tits theory","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Stephen DeBacker","submitted_at":"2023-09-16T17:15:45Z","abstract_excerpt":"Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\\mathbf{G}$ is a connected reductive $k$-group. If $\\mathbf{T}$ is a $K$-minisotropic maximal $k$-torus in $\\mathbf{G}$, then we use Bruhat-Tits theory to describe the stable classes in the $\\mathbf{G}$-orbit of $\\mathbf{T}$, the rational classes in the $\\mathbf{G}$-orbit of $\\mathbf{T}$, and the $k$-embeddings, up to rational conjugacy, into $\\mathbf{G}$ of $\\mathbf{T}$. We also provide, via Bruhat-Tits theory, a complete and explicit description of: the rational conjugacy classes of $K$-minisotr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09049","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.09049/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}