{"paper":{"title":"DG-resolutions of NC-smooth thickenings and NC-Fourier-Mukai transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Polishchuk, Junwu Tu","submitted_at":"2013-08-20T07:37:30Z","abstract_excerpt":"We give a construction of NC-smooth thickenings (a notion defined by Kapranov in math/9802041) of a smooth variety equipped with a torsion free connection. We show that a twisted version of this construction realizes all NC-smooth thickenings as 0th cohomology of a differential graded sheaf of algebras, similarly to Fedosov's construction in \\cite{Fed}. We use this dg resolution to construct and study sheaves on NC-smooth thickenings. In particular, we construct an NC version of the Fourier-Mukai transform from coherent sheaves on a (commutative) curve to perfect complexes on the canonical NC-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4244","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"}