Split Jacobians and Lower Bounds on Heights

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Split Jacobians and Lower Bounds on Heights

Type: Doctoral Thesis
Title: Split Jacobians and Lower Bounds on Heights
Author: Djukanovic, M.
Issue Date: 2017-11-01
Keywords: Split
Jacobian
Isogeny
Elliptic curve
Height
Bound
Lang
Silverman
Conjecture
Abstract: This thesis deals with properties of Jacobians of genus two curves that cover elliptic curves. If E is an elliptic curve and C is a curve of genus two that covers it n-to-1 so that the covering does not factor through an isogeny, then C also covers another elliptic curve n-to-1 in such a way and the Jacobian of C is isogenous to the product of the two elliptic curves. The Jacobian is said to be (n,n)-split and the elliptic curves are said to be glued along their n-torsion. The first chapter deals with the geometric aspects of this setup. We describe two approaches to constructing (n,n)-split Jacobians and we investigate which curves can appear in the setup. The second chapter deals with the arithmetic aspects, focusing on height functions and the Lang-Silverman conjecture in particular. We show that this conjecture holds for families of (n,n)-split Jacobians if and only if it holds for the corresponding families of elliptic curves that can be glued along their n-torsion.
Promotor: Supervisor: Edixhoven S.J. Co-Supervisor: Jong R.S. de, Pazuki F.M.
Faculty: Science
University: Leiden University and L'Université de Bordeaux
Handle: http://hdl.handle.net/1887/54944
 

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application/pdf Cover 61.45Kb View/Open
application/pdf Title Pages_Contents_Preface 426.4Kb View/Open
application/pdf Chapter 1 861.3Kb View/Open
application/pdf Chapter 2 608.8Kb View/Open
application/pdf Appendix_Bibliography 410.6Kb View/Open
application/pdf Summary in English 267.7Kb View/Open
application/pdf Summary in Dutch 268.2Kb View/Open
application/pdf Summary in Montenegrin 267.6Kb View/Open
application/pdf Acknowledgements_Curriculum Vitae 160.2Kb View/Open
application/pdf Propositions 171.1Kb View/Open

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