量子形變模上的兩個定理

Abstract

The theory of deformation quantization modules have a great improvement recently. In this thesis, we prove two basic theorems about this theory. The first theorem is a generalization of Riemann-Roch theorem for D-modules. We generalize the (algebraic) Riemann-Roch theorem for D-modules of [16] to (analytic) W -modules. The second theorem is a generalization of Serre's GAGA theorem [see 6]. Let X be a smooth complex projective variety with associated compact complex manifold X_{an}. If A_{X} is a DQ-algebroid on X, then there is an induced DQ-algebroid on X_{an}. We show that the natural functor from the derived category of bounded complexes of A_{X}-modules with coherent cohomologies to the derived category of bounded complexes of A_{X_{an}}-modules with coherent cohomologies is an equivalence.