{"paper":{"title":"On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Kei-ichiro Iima, Ryo Takahashi, Tokuji Araya","submitted_at":"2010-01-31T15:52:12Z","abstract_excerpt":"Let R be a complete local hypersurface over an algebraically closed field of characteristic different from two, and suppose that R has countable Cohen-Macaulay representation type. In this paper, it is proved that the maximal Cohen-Macaulay R-modules which are locally free on the punctured spectrum are dominated by the maximal Cohen-Macaulay R-modules which are not locally free on the punctured spectrum. More precisely, there exists a single R-module X such that the indecomposable maximal Cohen-Macaulay R-modules not locally free on the punctured spectrum are X and its syzygy \\Omega X and that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0137","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"}