{"paper":{"title":"Controlling the Dimensions of Formal Fibers of a Unique Factorization Domain at the Height One Prime Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David Schwein, Lena Ji, Nina Pande, Peter M. McDonald, Sarah M. Fleming, S. Loepp","submitted_at":"2016-01-26T19:15:50Z","abstract_excerpt":"Let T be a complete local (Noetherian) equidimensional ring with maximal ideal m such that the Krull dimension of T is at least two and the depth of T is at least two. Suppose that no integer of T is a zerodivisor and that |T|=|T/m|. Let d and t be integers such that 1 $\\leq$ d $\\leq$ dimT-1, 0 $\\leq$ t $\\leq$ dimT - 1, and d - 1 $\\leq$ t. Assume that, for every p in AssT, ht(p) $\\leq$ d-1 and that if z is a regular element of T and Q is in Ass(T/zT), then ht(Q) $\\leq$ d. We construct a local unique factorization domain A such that the completion of A is T and such that the dimension of the fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07136","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"}