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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 $\\le -n(d-1)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.03184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-11T02:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"b026e3f7edb3760a53ea5dec725ce5b3c3356bd73692c5adfd321aa4cddbb347","abstract_canon_sha256":"c342c17764f8e64633c30dbf8986e1dc747a349bf9fe7d6ef2f88d51070e3022"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:20.301260Z","signature_b64":"lAW0haL98MWY6zHGeiii1LMddyJLE4PiT4iUkPxRkz5Uols0PncCGj1bVuDUzXvulArrsfPIG5bHNdAqRw9LBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60042d1df295eb4ed2d9d52446b2420ff90f6af684c0eafbdd162450913cc029","last_reissued_at":"2026-05-18T02:27:20.300603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:20.300603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.03184","created_at":"2026-05-18T02:27:20.300725+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.03184v1","created_at":"2026-05-18T02:27:20.300725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03184","created_at":"2026-05-18T02:27:20.300725+00:00"},{"alias_kind":"pith_short_12","alias_value":"MACC2HPSSXVU","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MACC2HPSSXVU5UWZ","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MACC2HPS","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7","json":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7.json","graph_json":"https://pith.science/api/pith-number/MACC2HPSSXVU5UWZ2USENMSCB7/graph.json","events_json":"https://pith.science/api/pith-number/MACC2HPSSXVU5UWZ2USENMSCB7/events.json","paper":"https://pith.science/paper/MACC2HPS"},"agent_actions":{"view_html":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7","download_json":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7.json","view_paper":"https://pith.science/paper/MACC2HPS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.03184&json=true","fetch_graph":"https://pith.science/api/pith-number/MACC2HPSSXVU5UWZ2USENMSCB7/graph.json","fetch_events":"https://pith.science/api/pith-number/MACC2HPSSXVU5UWZ2USENMSCB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7/action/storage_attestation","attest_author":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7/action/author_attestation","sign_citation":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7/action/citation_signature","submit_replication":"https://pith.science/pith/MACC2HPSSXVU5UWZ2USENMSCB7/action/replication_record"}},"created_at":"2026-05-18T02:27:20.300725+00:00","updated_at":"2026-05-18T02:27:20.300725+00:00"}