Uniform Bogomolov Conjecture for Tori

authored by

Ruida Di

supervised by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Doctoral thesis

No. of pages

59

Publication date

14.08.2024

Publication status

Published

Electronic version(s)

https://doi.org/10.15488/17842 (Access: Open)