{"paper":{"title":"On the depth of tensor products over Cohen-Macaulay rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew J. Soto-Levins, Justin Lyle, Kaito Kimura","submitted_at":"2025-05-01T10:34:57Z","abstract_excerpt":"Inspired by classical work on the depth formula for tensor products of finitely generated $R$-modules, we introduce two conditions which we call $(\\mathbf{ldep})$ and $(\\mathbf{rdep})$ and their derived variations. We show for Cohen-Macaulay local rings that derived $(\\mathbf{ldep})$ is equivalent to $\\dim(R)$ being a uniform Auslander bound for $R$, and if $\\dim(R)>0$ that both are equivalent to $(\\mathbf{ldep})$. We introduce an analogous condition we call the \\emph{uniform Buchweitz condition} and provide a corresponding theorem for the $(\\mathbf{rdep})$ condition. As a consequence of these"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00441","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.00441/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}