{"paper":{"title":"Dimensions of automorphism group schemes of finite level truncations of $F$-cyclic $F$-crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiao Xiao, Zeyu Ding","submitted_at":"2018-12-09T23:19:27Z","abstract_excerpt":"Let $\\mathcal{M}_{\\pi}$ be an $F$-cyclic $F$-crystal $\\mathcal{M}_{\\pi}$ over an algebraically closed field defined by a permutation $\\pi$ and a set of prescribed Hodge slopes. We prove combinatorial formulas for the dimension $\\gamma_{\\mathcal{M}_{\\pi}}(m)$ of the automorphism group scheme of $\\mathcal{M}_{\\pi}$ at finite level $m$ and the number of connected components of the endomorphism group scheme of $\\mathcal{M}_{\\pi}$ at finite level $m$. As an application, we show that if $\\mathcal{M}_{\\pi}$ is a nonordinary Dieudonn\\'e module defined by a cycle $\\pi$, then $\\gamma_{\\mathcal{M}_{\\pi}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03577","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"}