Uniform Bogomolov Conjecture for Tori

verfasst von

Ruida Di

betreut von

Ziyang Gao

Abstract

The Bogomolov Conjecture for algebraic tori is a problem related to rational points on algebraic tori in Diophantine geometry. It inquires whether there are infinitely many non-torsion points with a canonical height tending to zero. The uniform version of this conjecture for algebraic tori was resolved in the 1990s. This dissertation presents a new proof inspired by the recent proof of the uniform Mordell-Lang Conjecture by Dimitrov-Gao-Habegger, Kühne, and Gao-Ge-Kühne.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Dissertation

Anzahl der Seiten

59

Publikationsdatum

14.08.2024

Publikationsstatus

Veröffentlicht

Elektronische Version(en)

https://doi.org/10.15488/17842 (Zugang: Offen)