{"paper":{"title":"Homology of powers of ideals: Artin--Rees numbers of syzygies and the Golod property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"J\\\"urgen Herzog, Siamak Yassemi, Volkmar Welker","submitted_at":"2011-08-30T08:04:04Z","abstract_excerpt":"For an ideal I in a regular local ring (R,m)$ with residue class field K = R/m or a standard graded K-algebra R we show that for k >> 0\n  --> the Artin--Rees number of the syzygy modules of I^k as submodules of the free modules from a free resolution is constant, and thereby present the Artin-Rees number as a proper replacement of regularity in the local situation,\n  --> the ring R/I^k is Golod, its Poincer{\\'e}-Betti series is rational and the Betti numbers of the free resolution of K over R/I^k are polynomials in k of a specific degree.\n  The first result is an extension of work of Kodiyalam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5862","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"}