量子形變模上的兩個定理

Two theorems for deformation quantization modules

陳厚伊(Hou-Yi Chen)

指導教授 ： 陳榮凱

國立臺灣大學/理學院/數學研究所/博士(2009年)

https://doi.org/10.6342/NTU.2009.03332

摘要

無資料

關鍵字

量子形變模

並列摘要

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.

並列關鍵字

deformation quantization modules

參考文獻

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