{"paper":{"title":"Uniform Artin-Rees Bounds for Syzygies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Aline Hosry, Ian M. Aberbach, Janet Striuli","submitted_at":"2014-06-11T11:56:33Z","abstract_excerpt":"Let $(R,m)$ be a local Noetherian ring, let $M$ be a finitely generated $R$-module and let $(F_{\\bullet},\\partial_{\\bullet})$ be a free resolution of $M$. We find a uniform bound $h$ such that the Artin-Rees containment $I^n F_i\\cap Im \\, \\partial_{i+1} \\subseteq I^{n-h} Im \\, \\partial_{i+1}$ holds for all integers $i\\ge d$, for all integers $n\\ge h$, and for all ideals $I$ of $R$. In fact, we show that a considerably stronger statement holds. The uniform bound $h$ holds for all ideals and all resolutions of $d$th syzygy modules. In order to prove our statements, we introduce the concept of Ko"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2866","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"}