{"paper":{"title":"The Frobenius morphism on flag varieties, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Samokhin","submitted_at":"2014-10-14T16:02:18Z","abstract_excerpt":"In this paper, given a semisimple algebraic group $\\bf G$ of rank 2, we construct a special semiorthogonal decomposition in the derived category of coherent sheaves on the flag variety ${\\bf G}/{\\bf B}$. These decompositions are defined over the localization ${\\mathbb Z}_{\\rm S}$, where $\\rm S$ is the set of bad primes for $\\bf G$, while their block structure is compatible with the Bruhat order on Schubert varieties. The non-standard $t$-structures on ${\\rm D}^b({\\bf G}/{\\bf B})$ defined by these decompositions are self-dual with respect to the duality ${\\mathcal RHom}_{{\\bf G}/{\\bf B}}(-,\\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3742","kind":"arxiv","version":3},"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"}