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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71225
標題: | 黎曼—羅赫定理的一個代數方法之證明 A Proof of Riemann-Roch Theorem by Algebraic Methods |
作者: | Hao-Wei Huang 黃皓偉 |
指導教授: | 蔡宜洵(I-Hsun Tsai) |
關鍵字: | 同調代數,指標定理, sheaf,homological algebra,spectral sequence,Riemann-Roch theorem, |
出版年 : | 2018 |
學位: | 碩士 |
摘要: | We start from some basic notions, like sheaves and cohomology, and try to introduce and prove Riemann-Roch theorem in the 2-dimension case. The definition of cohomology of a sheaf is more difficult to compute in some situation. However, the Čech cohomology of a sheaf over a paracompact space is isomorphic to the usual definition of cohomology,and Čech cohomology gives us a more concrete way to think what the cohomology of a sheaf is. In chapter 3 we introduce the concept of twisted complexes. We will use it to compute Ext and the class in Čech cohomology which is in the statement of Riemann-Roch theorem, and identify this class with characteristic class Td in cochain level by direct computation. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71225 |
DOI: | 10.6342/NTU201801660 |
全文授權: | 有償授權 |
顯示於系所單位: | 數學系 |
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ntu-107-1.pdf 目前未授權公開取用 | 2.33 MB | Adobe PDF |
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