{"paper":{"title":"Adic reduction to the diagonal and a relation between cofiniteness and derived completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Liran Shaul","submitted_at":"2016-02-11T20:31:33Z","abstract_excerpt":"We prove two results about the derived functor of $a$-adic completion: (1) Let $K$ be a commutative noetherian ring, let $A$ be a flat noetherian $K$-algebra which is $a$-adically complete with respect to some ideal $a\\subseteq A$, such that $A/a$ is essentially of finite type over $K$, and let $M,N$ be finitely generated $A$-modules. Then adic reduction to the diagonal holds: $A\\otimes^{L}_{ A\\hat{\\otimes}_{K} A } ( M\\hat{\\otimes}^{L}_{K} N ) \\cong M \\otimes^{L}_A N$. A similar result is given in the case where $M,N$ are not necessarily finitely generated. (2) Let $A$ be a commutative ring, l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03874","kind":"arxiv","version":3},"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"}