{"paper":{"title":"Support varieties of line bundle cohomology groups for SL3 (k)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"William D. Hardesty","submitted_at":"2014-08-10T21:16:55Z","abstract_excerpt":"Let $G= SL_3(k)$ where $k$ is a field of characteristic $p > 0$ and let $\\lambda \\in X(T)$ be any weight with corresponding line bundle $\\mathscr{L}(\\lambda)$ on $G/B$. In this paper we compute the support varieties for all modules of the form $H^i(\\lambda):= H^i(G/B, \\mathscr{L}(\\lambda))$ over the first Frobenius kernel $G_1$. The calculation involves certain recursive character formulas given by Donkin which can be used to compute the characters of the line bundle cohomology groups. In the case where $\\lambda$ is a $p$-regular weight and $M=H^i(\\lambda)\\neq 0$ for some $i$, these formulas a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2273","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"}