Huang Yong Dong. / Thesis submitted in: November 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 59-60). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Abelian Varieties And Shimura Varieties --- p.5 / Chapter 1.2 --- Jacobians of Some Families of Curves --- p.7 / Chapter 1.3 --- Endomorphism Algebras of Jacobians of Curves --- p.8 / Chapter 2 --- Families of Abelian Varieties --- p.11 / Chapter 2.1 --- Abelian Varieties --- p.11 / Chapter 2.2 --- The Endomorphism Algebra of A Simple Abelian Varieties --- p.13 / Chapter 2.3 --- Family of Abelian Varieties and Shimura Varieties --- p.15 / Chapter 2.3.1 --- Real Multiplication --- p.16 / Chapter 2.3.2 --- Totally Indefinite Quaternion Multiplication --- p.19 / Chapter 2.3.3 --- Totally Definite Quaternion Multiplication --- p.22 / Chapter 2.3.4 --- Complex Multiplication --- p.25 / Chapter 2.3.5 --- Shimura Varieties --- p.28 / Chapter 2.4 --- The Endomorphism Algebra of A General Member --- p.29 / Chapter 3 --- Jacobians of Some Families of Curves --- p.32 / Chapter 3.1 --- Some Families of Curves --- p.32 / Chapter 3.2 --- Kodaira-Spencer Map --- p.37 / Chapter 3.3 --- Infinity of CM Type Points --- p.46 / Chapter 3.3.1 --- Φ Is Dominant --- p.46 / Chapter 3.3.2 --- Infinity of CM Points --- p.50 / Chapter 4 --- Endomorphism Algebras of Jacobians of Some Fam- ilies of Curves --- p.51 / Chapter 4.1 --- Jacobians Between Finite Coverings of Curves --- p.51 / Chapter 4.2 --- Endomorphism Algebras of Families of Jacobians --- p.53 / Chapter 4.2.1 --- The Case For μ = 1 --- p.53 / Chapter 4.2.2 --- The Case For μ = 2 --- p.55 / Chapter 4.2.3 --- The Case For μ =3 --- p.58 / Bibliography
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324708 |
| Date | January 2004 |
| Contributors | Huang, Yong Dong., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 60 leaves : ill. ; 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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