Finiteness and duality
نویسندگان
چکیده
Consider a ring K, a topological space X and a sheaf A on X of K[[~]]-algebras. Assuming that A is ~-complete and without ~torsion, we first show how to deduce a coherency theorem for complexes of A -modules from a corresponding property for complexes of A /~A -modules. We apply this result to prove that, under a natural properness condition, the convolution of two coherent kernels over deformation quantization algebroids on complex Poisson manifolds is coherent. We also construct the dualizing complexes for such algebroids and show that the convolution of kernels commutes with duality. Mathematics Subject Classification: 53D55, 46L65, 32C38
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