{"paper":{"title":"Local cohomologies of isolated non F-rational singularities","license":"","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Yukihide Takayama","submitted_at":"2006-11-02T11:32:48Z","abstract_excerpt":"In this paper, we consider positively graded isolated non F-rational singularities (R,m) with d=dim R over the field K of positive characteristic.\n We give a representation of lower local cohomologies H^i_m(R) (i<d) in terms of tight closure and limit closure of certain type of parameters.\n As an application to isolated singularities, we show a relation between non-vanishing of the tight closure of zero in the highest local cohomology (0)^*_{H^d(R)} and non-vanishing of the cohomology H^{d-1}_m(R)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611047","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"}