by Leung Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 76-77). / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Elliptic curve --- p.4 / Chapter 2.1 --- Elliptic Curve in Normal Form --- p.4 / Chapter 2.2 --- Geometry and Group Law --- p.7 / Chapter 2.3 --- Special Class of Elliptic Curves --- p.10 / Chapter 2.4 --- Mordell's Conjecture --- p.12 / Chapter 2.5 --- Torsion Group --- p.14 / Chapter 2.6 --- Selmer Group and Tate-Shafarevitch. Group --- p.16 / Chapter 2.7 --- Endomorphism of Elliptic Curves --- p.19 / Chapter 2.8 --- Formal Group over Elliptic Curves --- p.23 / Chapter 2.9 --- The Finite Field Case --- p.26 / Chapter 2.10 --- The Local Field Case --- p.27 / Chapter 2.11 --- The Global Field Case --- p.29 / Chapter 3 --- Class Field Theory --- p.31 / Chapter 3.1 --- Valuation and Local Field --- p.31 / Chapter 3.2 --- Unramified and Totally Ramified Extensions and Their Norm Groups --- p.35 / Chapter 3.3 --- Formal Group and Abelian Extension of Local Field --- p.36 / Chapter 3.4 --- Abelian Extenion and Norm Residue Map --- p.41 / Chapter 3.5 --- Finite Extension and Ramification Group --- p.43 / Chapter 3.6 --- "Hilbert Symbols [α, β］w and (α, β)f" --- p.46 / Chapter 3.7 --- Adele and Idele --- p.48 / Chapter 3.8 --- Galois Extension and Kummer Extension --- p.50 / Chapter 3.9 --- Global Reciprocity Law and Global Class Field --- p.52 / Chapter 3.10 --- Ideal-Theoretic Formulation of Class Field Theory --- p.57 / Chapter 4 --- Hasse-Weil L-function of elliptic curves --- p.60 / Chapter 4.1 --- Classical Zeta Functions and L-functions --- p.60 / Chapter 4.2 --- Congruence Zeta Function --- p.63 / Chapter 4.3 --- Hasse-Weil L-function and Birch-Swinnerton-Dyer Conjecture --- p.64 / Chapter 4.4 --- A Sketch of the Proof from the Joint Paper of Coates and Wiles --- p.67 / Chapter 4.5 --- The works of other mathematicians --- p.73
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_319016 |
| Date | January 1992 |
| Contributors | Leung, Tak., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 77 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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