{"paper":{"title":"Faltings' local-global principle for the finiteness of local cohomology modules over Noetherian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Akbar Mehrvarz, Monireh Sedghi, Reza Naghipour","submitted_at":"2014-07-02T13:34:25Z","abstract_excerpt":"Let $R$ denote a commutative Noetherian (not necessarily local) ring, $\\frak a$ an ideal of $R$ and $M$ a finitely generated $R$-module. The purpose of this paper is to show that $f^n_{\\frak a}(M)=\\inf \\{0\\leq i\\in\\mathbb{Z}|\\, \\dim H^{i}_{\\frak a}(M)/N \\geq n\\, \\, \\text{for any finitely generated submodule}\\,\\, N \\subseteq H^{i}_{\\frak a}(M)\\}$, where $n$ is a non-negative integer and the invariant $f^n_{\\frak a}(M):=\\inf\\{f_{\\frak a R_{\\frak p}}(M_{\\frak p})\\,\\,|\\,\\,{\\frak p}\\in \\Supp M/\\frak a M\\,\\,{\\rm and}\\,\\,\\dim R/{\\frak p}\\geq n\\}$ is the $n$-th finiteness dimension of $M$ relative to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0559","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"}