{"paper":{"title":"A cohomological study of local rings of embedding codepth 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.AC","authors_text":"Luchezar L. Avramov","submitted_at":"2011-05-19T21:37:18Z","abstract_excerpt":"The generating series of the Bass numbers $\\mu^i_R=\\mathrm{rank}_k \\mathrm{Ext}^i_R(k,R)$ of local rings $R$ with residue field $k$ are computed in closed rational form, in case the embedding dimension $e$ of $R$ and its depth $d$ satisfy $e-d\\le 3$. For each such $R$ it is proved that there is a real number $\\gamma>1$, such that $\\mu^{d+i}_R\\ge\\gamma\\mu^{d+i-1}_R$ holds for all $i\\ge 0$, except for $i=2$ in two explicitly described cases, where $\\mu^{d+2}_R=\\mu^{d+1}_R=2$. New restrictions are obtained on the multiplicative structures of minimal free resolutions of length 3 over regular local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3991","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"}