| dc.contributor.advisor | Schindler, Damaris Prof. Dr. | |
| dc.contributor.author | Munkelt, Florian Maximilian | |
| dc.date.accessioned | 2023-11-10T18:02:40Z | |
| dc.date.available | 2023-11-17T00:50:12Z | |
| dc.date.issued | 2023-11-10 | |
| dc.identifier.uri | http://resolver.sub.uni-goettingen.de/purl?ediss-11858/14970 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-10191 | |
| dc.format.extent | 85 | de |
| dc.language.iso | eng | de |
| dc.subject.ddc | 510 | de |
| dc.title | Diophantine problems: inequalities and abelian varieties | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Schindler, Damaris Prof. Dr. | |
| dc.date.examination | 2023-06-09 | de |
| dc.description.abstracteng | In 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 point. | de |
| dc.contributor.coReferee | Brüdern, Jörg Prof. Dr. | |
| dc.contributor.thirdReferee | Lombardo, Davide Dr. | |
| dc.subject.eng | Number theory | de |
| dc.subject.eng | Diophantine equations | de |
| dc.subject.eng | Diophantine inequalities | de |
| dc.subject.eng | Abelian varieties | de |
| dc.subject.eng | Uniform Boundedness Conjecture | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-ediss-14970-9 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.description.embargoed | 2023-11-17 | de |
| dc.identifier.ppn | 1871667011 | |
| dc.notes.confirmationsent | Confirmation sent 2023-11-10T19:45:01 | de |