Mak, Kit Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 78-81). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.7 / Chapter 2 --- Preliminaries on Number Theory --- p.10 / Chapter 2.1 --- Finite Fields --- p.10 / Chapter 2.2 --- p-adic Numbers --- p.13 / Chapter 2.3 --- The Teichmuller Representatives --- p.16 / Chapter 2.4 --- Character Theory --- p.18 / Chapter 3 --- Basic Calabi-Yau Geometry --- p.26 / Chapter 3.1 --- Definition and Basic Properties of Calabi-Yau Manifolds --- p.26 / Chapter 3.2 --- Calabi-Yau Manifolds of Low Dimensions --- p.29 / Chapter 3.3 --- Constructions of Calabi-Yau Manifolds --- p.32 / Chapter 3.4 --- Importance of Calabi-Yau Manifolds in Physics --- p.35 / Chapter 4 --- Number of Points on Calabi-Yau Manifolds over Finite Fields --- p.39 / Chapter 4.1 --- The General Method --- p.39 / Chapter 4.2 --- The Number of Points on a Family of Calabi-Yau Varieties over Finite Fields --- p.45 / Chapter 4.2.1 --- The Case ψ = 0 --- p.45 / Chapter 4.2.2 --- The Case ψ ß 0 --- p.50 / Chapter 4.3 --- The Number of Points on the Affine Mirrors over Finite Fields --- p.55 / Chapter 4.3.1 --- The Case ψ = 0 --- p.55 / Chapter 4.3.2 --- The Case ψ ß 0 --- p.56 / Chapter 4.4 --- The Number of points on the Projective Mirror over Finite Fields --- p.59 / Chapter 4.5 --- Summary of the Results and Related Conjectures --- p.61 / Chapter 5 --- The Relation Between Periods and the Number of Points over Finite Fields modulo q --- p.67 / Chapter 5.1 --- Periods of Calabi-Yau Manifolds --- p.67 / Chapter 5.2 --- The Case for Elliptic Curves --- p.69 / Chapter 5.2.1 --- The Periods of Elliptic Curves --- p.69 / Chapter 5.2.2 --- The Number of Fg-points on Elliptic Curves Modulo q --- p.70 / Chapter 5.3 --- The Case for a Family of Quintic Threefolds --- p.73 / Chapter 5.3.1 --- The Periods of Xψ --- p.73 / Chapter 5.3.2 --- The Number of F9-points on Quintic Three- folds Modulo q --- p.75 / Bibliography --- p.78
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326301 |
| Date | January 2008 |
| Contributors | Mak, Kit Ho., 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, 81 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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