{"paper":{"title":"A new proof of Faltings' local-global principle for the finiteness of local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Davood Asadollahi, Reza Naghipour","submitted_at":"2014-06-05T10:23:44Z","abstract_excerpt":"Let $R$ denote a commutative Noetherian ring. Brodmann et al. defined and studied the concept of the local-global principle for annihilation of local cohomology modules at level $r\\in\\mathbb{N}$ for the ideals $\\frak a$ and $\\frak b$ of $R$. It was shown that this principle holds at levels 1,2, over $R$ and at all levels whenever $\\dim R\\leq 4$. The goal of this paper is to show that, if the set $\\Ass_R(H_{\\fa}^{f_{\\fa}^{\\fb}(M)}(M))$ is finite or $f_{\\fa}(M)\\neq c_{\\fa}^{\\fb}(M)$, then the local-global principle holds at all levels $r\\in\\mathbb{N}_0$, for all ideals $\\fa, \\fb$ of $R$ and each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1323","kind":"arxiv","version":2},"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"}