{"paper":{"title":"New graded methods in the homological algebra of semisimple algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian J. Parshall, Leonard L. Scott","submitted_at":"2013-04-04T18:43:25Z","abstract_excerpt":"Let $G$ be a semisimple algebraic group over an algebraically closed field $k$ of positive characteristic $p$. Under some restrictions on the size of $p$, the present paper establishes new results on the $G$-module structure of $\\Ext^\\bullet_{G_1}(V,W)$ when $V,W$ belong to several important classes of rational $G$-modules, and $G_1$ denotes the first Frobenius kernel of $G$. For example, it is proved that, if $L,L'$ are ($p$-regular) irreducible $G_1$-modules, then $\\Ext^n_{G_1}(L,L')^{[-1]}$ has a good filtration with computable multiplicities. This and many other results depend on the entir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1461","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"}