{"paper":{"title":"On the finiteness properties of local cohomology modules for regular local rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Monireh Sedghi, Reza Naghipour","submitted_at":"2017-03-02T12:26:54Z","abstract_excerpt":"Let $\\frak a$ denote an ideal in a regular local (Noetherian) ring $R$ and let $N$ be a finitely generated $R$-module with support in $V(\\frak a)$. The purpose of this paper is to show that all homomorphic images of the $R$-modules $\\Ext^j_R(N, H^i_{\\frak a}(R))$ have only finitely many associated primes, for all $i, j\\geq 0$, whenever $\\dim R \\leq4$ or $\\dim R/ \\frak a \\leq 3$ and $R$ contains a field. In addition, we show that if $\\dim R=5$ and $R$ contains a field, then the $R$-modules $\\Ext^j_R(N, H^i_{\\frak a}(R))$ have only finitely many associated primes, for all $i, j\\geq 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00756","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"}