{"paper":{"title":"On Universal Deformation Rings for Gorenstein Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2016-04-01T22:38:41Z","abstract_excerpt":"Let $\\mathbf{k}$ be an algebraically closed field, and let $\\Lambda$ be a finite dimensional $\\mathbf{k}$-algebra. We prove that if $\\Lambda$ is a Gorenstein algebra, then every finitely generated Cohen-Macaulay $\\Lambda$-module $V$ whose stable endomorphism ring is isomorphic to $\\mathbf{k}$ has a universal deformation ring $R(\\Lambda,V)$, which is a complete local commutative Noetherian $\\mathbf{k}$-algebra with residue field $\\mathbf{k}$, and which is also stable under taking syzygies. We investigate a particular non-self-injective Gorenstein algebra $\\Lambda_0$, which is of infinite global"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00429","kind":"arxiv","version":2},"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"}