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A survey on Calabi-Yau manifolds over finite fields.

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

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326301
Date January 2008
ContributorsMak, Kit Ho., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 81 leaves : ill. ; 30 cm.
RightsUse 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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