Diophantine and Arithmetic Geometry
Third-party funded project
Project title Diophantine and Arithmetic Geometry
Principal Investigator(s) Kühne, Lars
Organisation / Research unit Departement Mathematik und Informatik / Zahlentheorie (Habegger)
Project start 01.07.2017
Probable end 30.06.2020
Status Completed

This research project is at the crossroads of diophantine geometry and arithmetic algebraic geometry. The overall leitmotif is to understand how geometry and arithmetic are intertwined in certain objects, be these of a purely diophantine nature, such as algebraic varieties over number fields, or of an arithmetic-geometric nature, such as families of abelian varieties and Shimura varieties. The project features roughly four different lines of research. First, some problems related to the André-Oort conjecture are studied. Second, there is some follow-up work on my recent proof of the Bounded Height Conjecture for general semiabelian varieties. Third, I aim to prove a certain conjecture in (p-adic) anabelian geometry. Finally, the behavior of the Faltings height in certain settings will be investigated.

Keywords André-Oort-Vermutung; Höhentheorie; diophantische Geometrie; arithmetische algebraische Geometry; anabelsche Geometrie; Faltingshöhe; Höhenschranken; Höhenschrankenvermutung
Financed by Swiss National Science Foundation (SNSF)

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