{"paper":{"title":"Non-Commutative Resolutions of Toric Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.AC","authors_text":"Eleonore Faber, Greg Muller, Karen E. Smith","submitted_at":"2018-05-01T18:00:20Z","abstract_excerpt":"Let $R$ be the coordinate ring of an affine toric variety. We show that the endomorphism ring $End_R(\\mathbb A),$ where $\\mathbb A$ is the (finite) direct sum of all (isomorphism classes of) conic $R$-modules, has finite global dimension. Furthermore, we show that $End_R(\\mathbb A)$ is a non-commutative crepant resolution if and only if the toric variety is simplicial. For toric varieties over a perfect field $k$ of prime characteristic, we show that the ring of differential operators $D_\\mathsf{k}(R)$ has finite global dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00492","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"}