{"paper":{"title":"Universal Deformation Rings for Complexes over Finite-Dimensional 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":"2017-03-24T18:42:55Z","abstract_excerpt":"Let $\\mathbf{k}$ be field of arbitrary characteristic and let $\\Lambda$ be a finite dimensional $\\mathbf{k}$-algebra. From results previously obtained by F.M Bleher and the author, it follows that if $V^\\bullet$ is an object of the bounded derived category $\\mathcal{D}^b(\\Lambda\\textup{-mod})$ of $\\Lambda$, then $V^\\bullet$ has a well-defined versal deformation ring $R(\\Lambda, V^\\bullet)$, which is complete local commutative Noetherian $\\mathbf{k}$-algebra with residue field $\\mathbf{k}$, and which is universal provided that $\\textup{Hom}_{\\mathcal{D}^b(\\Lambda\\textup{-mod})}(V^\\bullet, V^\\bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08569","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"}