{"paper":{"title":"Regularity and linearity defect of modules over local rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maria Evelina Rossi, Rasoul Ahangari Maleki","submitted_at":"2013-09-18T05:14:34Z","abstract_excerpt":"Given a finitely generated module $M$ over a commutative local ring (or a standard graded $k$-algebra) $(R,\\m,k) $ we detect its complexity in terms of numerical invariants coming from suitable $\\m$-stable filtrations $\\mathbb{M}$ on $M$. We study the Castelnuovo-Mumford regularity of $gr_{\\mathbb{M}}(M) $ and the linearity defect of $M,$ denoted $\\ld_R(M),$ through a deep investigation based on the theory of standard bases. If $M$ is a graded $R$-module, then $\\reg_R(gr_{\\mathbb{M}}(M)) <\\infty$ implies $\\reg_R(M)<\\infty$ and the converse holds provided $M$ is of homogenous type. An analogous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4538","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"}