{"paper":{"title":"Attached primes of local cohomology modules under localization and completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Le Thanh Nhan, Pham Hung Quy","submitted_at":"2014-04-01T02:44:40Z","abstract_excerpt":"Let $(R,\\m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. Following I. G. Macdonald \\cite{Mac}, the set of all attached primes of the Artinian local cohomology module $H^i_{\\m}(M)$ is denoted by $\\Att_R(H^i_{\\m}(M))$. In \\cite[Theorem 3.7]{Sh}, R. Y. Sharp proved that if $R$ is a quotient of a Gorenstein local ring then the shifted localization principle always holds true, i.e. $$ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\Att_{R_{\\p}}\\big(H^{i-\\dim (R/\\p)}_{\\p R_{\\p}}(M_{\\p})\\big)=\\big\\{\\q R_{\\p}\\mid \\q\\in\\Att_RH^i_{\\m}(M), \\q\\subseteq \\p\\big\\} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0111","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"}