{"paper":{"title":"Purity of Crystalline Strata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrian vasiu, Jinghao Li","submitted_at":"2018-01-29T16:01:01Z","abstract_excerpt":"Let $p$ be a prime. Let $n\\in\\mathbb N-\\{0\\}$. Let $\\mathcal C$ be an $F^n$-crystal over a locally noetherian $\\mathbb F_p$-scheme $S$. Let $(a,b)\\in\\mathbb N^2$. We show that the reduced locally closed subscheme of $S$ whose points are exactly those $x\\in S$ such that $(a,b)$ is a break point of the Newton polygon of the fiber $\\mathcal C_x$ of $\\mathcal C$ at $x$ is pure in $S$, i.e., it is an affine $S$-scheme. This result refines and reobtains previous results of de Jong--Oort, Vasiu, and Yang. As an application, we show that for all $m\\in \\mathbb N$ the reduced locally closed subscheme of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09593","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"}