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Diophantine problems: inequalities and abelian varieties

dc.contributor.advisorSchindler, Damaris Prof. Dr.
dc.contributor.authorMunkelt, Florian Maximilian
dc.titleDiophantine problems: inequalities and abelian varietiesde
dc.contributor.refereeSchindler, Damaris Prof. Dr.
dc.description.abstractengIn this thesis we consider the density of rational points near manifolds and a bound for the torsion on a simple abelian variety of type IV over a number field. In the first part the main result is an asymptotic for the number of rational points close to a compact parametrized manifold under a significantly weaker curvature condition than previous authors considered. In the second part, which is joined work with Victoria Cantoral-Farfan, we study the torsion subgroup of the Mordell-Weil group of a simple abelian variety of type IV. An optimal exponent is established to give a bound for the order of the torsion subgroup for a finite extension of the base field in terms of the extension degree. As a consequence we obtain a lower bound for the degree of an extension generated by a torsion
dc.contributor.coRefereeBrüdern, Jörg Prof. Dr.
dc.contributor.thirdRefereeLombardo, Davide Dr.
dc.subject.engNumber theoryde
dc.subject.engDiophantine equationsde
dc.subject.engDiophantine inequalitiesde
dc.subject.engAbelian varietiesde
dc.subject.engUniform Boundedness Conjecturede
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.notes.confirmationsentConfirmation sent 2023-11-10T19:45:01de

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