{"paper":{"title":"On Bruhat-Tits theory over a higher dimensional base","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Vikraman Balaji, Yashonidhi Pandey","submitted_at":"2022-03-17T16:33:21Z","abstract_excerpt":"Let $k$ be a perfect field. Assume that the characteristic of $k$ satisfies certain tameness assumptions \\eqref{tameness}. Let $\\mathcal O_{_n} := k\\llbracket z_{_1}, \\ldots, z_{_n}\\rrbracket$ and set $K_{_n} := \\text{Fract}~\\cO_{_n}$. Let $G$ be an almost-simple, simply-connected affine Chevalley group scheme with a maximal torus $T$ and a Borel subgroup $B$. Given a $n$-tuple ${\\bf f} = (f_{_1}, \\ldots, f_{_n})$ of concave functions on the root system of $G$ as in Bruhat-Tits \\cite{bruhattits1}, \\cite{bruhattits}, we define {\\it {\\tt n}-bounded subgroups ${\\tt P}_{_{\\bf f}}\\subset G(K_{_n})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.09431","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.09431/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"}