{"paper":{"title":"A Note on Injectivity of Frobenius on Local Cohomology of Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Eric Canton","submitted_at":"2015-02-11T02:57:21Z","abstract_excerpt":"Let $k$ be a field of characteristic $p > 0$ such that $[k:k^p] < \\infty$ and let $f \\in R = k[x_0, ..., x_n]$ be homogeneous of degree $d$. We obtain a sharp bound on the degrees in which the Frobenius action on $H^n_\\mathfrak{m}(R/fR)$ can be injective when $R/fR$ has an isolated non-F-pure point at $\\mathfrak{m}$. As a corollary, we show that if $(R/fR)_\\mathfrak{m}$ is not F-pure then $R/fR$ has an isolated non-F-pure point at $\\mathfrak{m}$ if and only if the Frobenius action is injective in degrees $\\le -n(d-1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03184","kind":"arxiv","version":1},"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"}