{"paper":{"title":"Castelnuovo-Mumford regularity and cohomological dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Maryam Jahangiri","submitted_at":"2013-04-09T10:27:10Z","abstract_excerpt":"Let $R=\\oplus_{i\\in \\N_0}R_n$ be a standard graded ring, $R_+ :=\\oplus_{i\\in \\N}R_n$ be the irrelevant ideal of $R$ and $\\fa_0$ be an ideal of $R_0$. In this paper, as a generalization of the concept of Castelnouvo-Mumford regularity $\\reg(M)$ of a finitely generated graded $R$-module $M$, we define the regularity of $M$ with respect to $\\fa_0+ R_+$, say $\\reg_{\\fa_0+ R_+}(M)$. And we study some relations of this new invariant with the classic one. To this end, we need to consider the cohomological dimension of some finitely generated $R_0$-modules. Also, we will express $\\reg_{\\fa_0+ R_+}(M)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2517","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"}