The CM class number one problem for curves

Leiden Repository

The CM class number one problem for curves

Type: Doctoral Thesis
Title: The CM class number one problem for curves
Author: Kilicer, P.
Issue Date: 2016-07-05
Keywords: Complex multiplication
CM curves
Class number one
Field of definition
Abstract: The main subject of this thesis is the CM class number one problem for curves of genus g, in the cases g=2 and g=3. The problem asks for which CM fields of degree 2g with a primitive CM type are the corresponding CM curves of genus g defined over the reflex field. Chapter 1 is an introduction to abelian varieties and complex multiplication theory. We present facts that we will use in later chapters. The results in this chapter are mostly due to Shimura and Taniyama. Chapter 2 is a joint work with Marco Streng, we give a solution to the CM class number one problem for curves of genus 2. Chapter 3 deals with the CM class number one problem for curves of genus 3. We give a partial solution to this problem. We restrict ourselves to the case where the sextic CM field corresponding to such a curve contains an imaginary quadratic subfield. Chapter 4 gives the complete list of sextic CM fields K for which there exist principally polarized simple abelian threefolds that has CM by the maximal order of K with rational field of moduli.
Promotor: Supervisor: P. Stevenhagen, A. Enge Co-Supervisor: T.C. Streng
Faculty: Science
University: Leiden University and l'Université de Bordeaux I
Handle: http://hdl.handle.net/1887/41145
 

Files in this item

Description Size View
application/pdf Full Text 1.552Mb View/Open
application/pdf Cover 202.0Kb View/Open
application/pdf Title Pages_Contents_Preface 967.3Kb View/Open
application/pdf Chapter 1 478.4Kb View/Open
application/pdf Chapter 2 493.7Kb View/Open
application/pdf Chapter 3 520.3Kb View/Open
application/pdf Chapter 4 319.0Kb View/Open
application/pdf Bibliography 256.3Kb View/Open
application/pdf Summary in English 215.3Kb View/Open
application/pdf Summary in Dutch 215.9Kb View/Open
application/pdf Summary in French 216.1Kb View/Open
application/pdf Acknowledgements_Curriculum Vitae 138.9Kb View/Open
application/pdf Propositions 157.7Kb View/Open

This item appears in the following Collection(s)