Duality and Equivalence of Module Categories in Noncommutative Geometry
نویسنده
چکیده
We develop a general framework to describe dualities from algebraic, differential, and noncommutative geometry, as well as physics. We pursue a relationship between the Baum-Connes conjecture in operator K-theory and derived equivalence statements in algebraic geometry and physics. We associate to certain data, reminiscent of spectral triple data, a differential graded category in such a way that we can recover the derived category of coherent sheaves on a complex manifold.
منابع مشابه
Duality and Equivalence of Module Categories in Noncommutative Geometry Ii: Mukai Duality for Holomorphic Noncommutative Tori
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