{"paper":{"title":"The Frobenius morphism in invariant theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA","math.RT"],"primary_cat":"math.AG","authors_text":"Michel Van den Bergh, Theo Raedschelders, \\v{S}pela \\v{S}penko","submitted_at":"2017-05-04T13:23:12Z","abstract_excerpt":"Let $R$ be the homogeneous coordinate ring of the Grassmannian $\\mathbb{G}=\\operatorname{Gr}(2,n)$ defined over an algebraically closed field of characteristic $p>0$. In this paper we give a completely characteristic free description of the decomposition of $R$, considered as a graded $R^p$-module, into indecomposables (\"Frobenius summands\"). As a corollary we obtain a similar decomposition for the Frobenius pushforward of the structure sheaf of $\\mathbb{G}$ and we obtain in particular that this pushforward is almost never a tilting bundle. On the other hand we show that $R$ provides a \"noncom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01832","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":""},"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"}