Duality and equivalence of module categories in noncommutative geometry II: Mukai duality for holomorphic noncommutative tori

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dc.creatorBlock, Jonathan
dc.date2006-04-12
dc.date.accessioned2026-07-07T07:10:52Z
dc.date.available2026-07-07T07:10:52Z
dc.descriptionThis is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In \cite{mem} we introduced the basic DG category $\Pc_{\A^\bullet}$, the perfect category of $\A^\bullet$, which corresponded to the category of coherent sheaves on a complex manifold. In this paper we enlarge this category to include objects which correspond to quasi-coherent sheaves. We then apply this framework to proving an equivalence of categories between derived categories on the noncommutative complex torus and on a holomorphic gerbe on the dual complex torus.
dc.identifierhttps://arxiv.org/abs/math/0604296
dc.identifierhttp://arxiv.org/abs/math/0604296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111556
dc.subjectQuantum Algebra
dc.subjectDifferential Geometry
dc.subject46L87, 14A22; 53D55; 14A20; 58B34
dc.titleDuality and equivalence of module categories in noncommutative geometry II: Mukai duality for holomorphic noncommutative tori
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