{"paper":{"title":"Faltings' Local-global Principle and Annihilator Theorem for the finiteness dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mohammad Reza Doustimehr","submitted_at":"2017-12-25T13:26:37Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring, $M$ a finitely generated $R$-module and $n$ be a non-negative integer. In this article, it is shown that there is a finitely generated submodule $N_i$ of $H_{\\frak a}^i(M)$ such that $\\dim{\\rm Supp } H_{\\frak a}^i(M)/N_i<n$ for all $i<t$ if and only if there is a finitely generated submodule $N_{i,{\\frak p}}$ of $H_{{\\frak a} R_{\\frak p}}^i(M_{\\frak p})$ such that $\\dim{\\rm Supp } H_{{\\frak a} R_{\\frak p}}^i(M_{\\frak p})/N_{i,{\\frak p}}<n$ for all $i<t$. This generalizes Faltings' Local-global Principle for the finiteness of local cohomology modules (F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09067","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"}