{"paper":{"title":"Matrix factorizations over elementary divisor domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.AC","authors_text":"Calin Iuliu Lazaroiu, Dmitry Doryn, Mehdi Tavakol","submitted_at":"2018-02-21T16:09:31Z","abstract_excerpt":"We study the homotopy category $\\mathrm{hmf}(R,W)$ of matrix factorizations of non-zero elements $W\\in R^\\times$, where $R$ is an elementary divisor domain. When $R$ has prime elements and $W$ factors into a square-free element $W_0$ and a finite product of primes of multiplicity greater than one and which do not divide $W_0$, we show that $\\mathrm{hmf}(R,W)$ is triangle-equivalent with an orthogonal sum of the triangulated categories of singularities $\\mathrm{D}_{\\mathrm sing}(A_n(p))$ of the local Artinian rings $A_n(p)=R/\\langle p^n\\rangle$, where $p$ runs over the prime divisors of $W$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07635","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"}