{"paper":{"title":"Depth formula via complete intersection flat dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Parviz Sahandi, Siamak Yassemi, Tirdad Sharif","submitted_at":"2010-08-10T05:46:07Z","abstract_excerpt":"We prove the depth formula, for homologically bounded complexes $X, Y$ provided that the complete intersection flat dimension of $X$ is finite and $\\sup(X\\utp_RY)<\\infty$. In particular, let $M$ and $N$ are two $R$-modules and the complete intersection flat dimension of $M$ is finite. Then $M$ and $N$ satisfies the depth formula, provided $\\Tor^R_i(M,N)=0$ for all $i\\ge 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1637","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"}