{"paper":{"title":"Maximal Cohen-Macaulay modules over local toric rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hans Schoutens","submitted_at":"2014-08-26T19:48:52Z","abstract_excerpt":"In analogy with the classical, affine toric rings, we define a local toric ring as the quotient of a regular local ring modulo an ideal generated by binomials in a regular system of parameters with unit coefficients; if the coefficients are just $\\pm1$, we call the ring purely toric.\n  We prove the following results on the existence of MCM's (=maximal Cohen-Macaulay modules): (EQUI$\\mathstrut_p$) we construct certain families of local toric rings satisfying Hochster's small MCM conjecture in positive characteristic; (EQUI$\\mathstrut_0$) provided Hochster's small MCM conjecture holds in positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6220","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"}