{"paper":{"title":"Highest weight category structures on $rep(B)$ and full exceptional collections on generalized flag varieties over $\\mathbb Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Samokhin, Wilberd van der Kallen","submitted_at":"2024-07-18T16:30:35Z","abstract_excerpt":"Given a split simply connected and connected algebraic group scheme $\\mathbb G$ over $\\mathbb Z$ and a split parabolic subgroup scheme $\\mathbb P\\subset \\mathbb G$, this paper constructs semi-orthogonal decompositions of the bounded derived category $D^b(\\mathrm {rep}( \\mathbb P))$ of noetherian representations of $\\mathbb P$ with each semi-orthogonal component being equivalent to the bounded derived category $D^b(\\mathrm {rep}( \\mathbb G))$ of noetherian representations of $\\mathbb G$. The semi-orthogonal components of those decompositions are stable under the monoidal action of $D^b(\\mathrm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13653","kind":"arxiv","version":4},"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/2407.13653/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"}