{"paper":{"title":"On the Existence of Mock Injective Modules for Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel K. Nakano, Paul Sobaje, William D. Hardesty","submitted_at":"2016-04-13T15:46:48Z","abstract_excerpt":"Let $G$ be an affine algebraic group scheme over an algebraically closed field $k$ of characteristic $p>0$, and let $G_r$ denote the $r$-th Frobenius kernel of $G$. Motivated by recent work of Friedlander, the authors investigate the class of mock injective $G$-modules, which are defined to be those rational $G$-modules that are injective on restriction to $G_r$ for all $r\\geq 1$. In this paper the authors provide necessary and sufficient conditions for the existence of non-injective mock injective $G$-modules, thereby answering a question raised by Friedlander. Furthermore, the authors invest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03840","kind":"arxiv","version":2},"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"}