{"paper":{"title":"Purity Results on $F$-crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jinghao Li","submitted_at":"2014-11-18T00:27:18Z","abstract_excerpt":"For an $F^n$-crystal $\\mathfrak C$ over a reduced locally Noetherian $\\mathbb F_p$-scheme $S$, Vasiu first obtained the purity of the Newton polygon strata of $S$ defined by $\\mathfrak C$. Deligne later obtained the purity of the $p$-rank strata of $S$ defined by $\\mathfrak C$. We prove a stronger result that for every fixed point $P_0$ in the $xy$-coordinate plane, the reduced locally closed subscheme $S_{P_0}=\\{s\\in S| NP(\\mathfrak C_s)\\mbox{ has }P_0\\mbox{ as a break point}\\}$ of $S$ is pure in $S$ (A weaker result was known for the weak purity of $S_{p_0}$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4699","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"}