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Multiplication polynomials and relative Manin-Mumford

Schmidt, Harry. Multiplication polynomials and relative Manin-Mumford. 2015, PhD Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_11526

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Abstract

After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is
$(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the discriminant of the
 curve. In the appendix we give an application to good reduction of an associated Latt\`es map. We also prove a similar result for the discriminant of the largest square free factor of $B_n$.
In the third chapter we prove a Manin-Mumford type result for additive extensions of elliptic families over the field of all complex numbers. We show in the appendix that there are finiteness consequences for Pell's equation over polynomial rings and integration in elementary terms. Our work can be made effective because we use counting results only for analytic curves.

Advisors:Masser, David William and Bertrand, Daniel
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser)
Item Type:Thesis
Thesis no:11526
Bibsysno:Link to catalogue
Number of Pages:1 Online-Ressource
Language:English
Identification Number:
Last Modified:30 Jun 2016 10:59
Deposited On:04 Feb 2016 09:37

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