黎曼—羅赫定理的一個代數方法之證明

Hao-Wei Huang; 黃皓偉

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71225

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DC 欄位	值	語言
dc.contributor.advisor	蔡宜洵(I-Hsun Tsai)
dc.contributor.author	Hao-Wei Huang	en
dc.contributor.author	黃皓偉	zh_TW
dc.date.accessioned	2021-06-17T04:59:35Z	-
dc.date.available	2021-08-01
dc.date.copyright	2018-08-01
dc.date.issued	2018
dc.date.submitted	2018-07-26
dc.identifier.citation	1. Schechtman, V. V. , Riemann-Roch theorem after D. Toledo and Y.-L. Tong. Proceedings of the Winter School Geometry and Physics. Palermo: Circolo Matematico di Palermo, [53]-81,1989. 2. Toledo, D. , Tong, Y. L. , A parametrix for overline partial and Riemann-Roch in Cech theory. Topology, v. 15, 1976. 3. Toledo,D. , Tong, Y. L. , Duality and intersection theory in complex manifolds. I. Math. Ann. 237, 1978. 4. O'Brian, N. , Toledo, D. , Tong, Y. L. , The trace map and characteristic classes for coherent sheaves. Amer. J. Math. 103, 1981. 5. O'Brian, N. , Toledo, D. , Tong, Y. L. , Hirzebruch-Riemann-Roch for coherent sheaves. Ibid. , 103, 1981. 6. Hartshorne, R. , Algebraic Geometry. Springer, 1977. 7. Huybrechts, D. , Complex Geometry An introduction. Springer-Verlag Berlin Heidelberg, 2005. 8. Weibel, C. A. , An Introduction to Homological Algebra. Cambridge University Press, 1994. 9. Griffiths, P. , Harris, J. , Principles of Algebraic Geometry. John Wiley & Sons, 1978. 10. Eisenbud, D. , Harris, J. , The Geometry of Scheme. Springer-Verlag New York, 2000, 17. 11. Grothendieck, A. , Théorèmes de dualité pour les faisceaux algébriques cohérents. Séminaire Bourbaki, t. 9, 1956-1957, No. 149.
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71225	-
dc.description.abstract	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.	en
dc.description.provenance	Made available in DSpace on 2021-06-17T04:59:35Z (GMT). No. of bitstreams: 1 ntu-107-R04221010-1.pdf: 2386480 bytes, checksum: c5662079e9bd0c29d87cef8df57e1609 (MD5) Previous issue date: 2018	en
dc.description.tableofcontents	口試委員會審定書 i 中文摘要 ii 英文摘要 iii Chapter 1 Introduction 1 Chapter 2 Sheaves Cohomology 2 2.1 Derived functors 2 2.2 Sheaves 3 2.3 Čech cohomology 8 Chapter 3 Duality 11 3.1 Ext group 11 3.2 Gysin map 13 Chapter 4 Homological technique 16 4.1 Spectral sequences 16 4.2 Koszul complex 20 4.3 Twisted complexes 23 Chapter 5 Local calculations 27 5.1 Constructions of 1-cocycle 27 5.2 Computing the class 31 參考文獻 39
dc.language.iso	en
dc.subject	同調代數	zh_TW
dc.subject	指標定理	zh_TW
dc.subject	sheaf	en
dc.subject	homological algebra	en
dc.subject	spectral sequence	en
dc.subject	Riemann-Roch theorem	en
dc.title	黎曼—羅赫定理的一個代數方法之證明	zh_TW
dc.title	A Proof of Riemann-Roch Theorem by Algebraic Methods	en
dc.type	Thesis
dc.date.schoolyear	106-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	陳榮凱(Jung-Kai Chen),黃一樵(I-Chiao Huang)
dc.subject.keyword	同調代數,指標定理,	zh_TW
dc.subject.keyword	sheaf,homological algebra,spectral sequence,Riemann-Roch theorem,	en
dc.relation.page	39
dc.identifier.doi	10.6342/NTU201801660
dc.rights.note	有償授權
dc.date.accepted	2018-07-26
dc.contributor.author-college	理學院	zh_TW
dc.contributor.author-dept	數學研究所	zh_TW
顯示於系所單位：	數學系

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