Explicit height bounds and the explicit Mordell-Lang Conjecture

2016/09/15 by Viada, Evelina
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.04607

Abstract

We give an overview of some landmark theorems and recent conjectures in Diophantine Geometry. In the elliptic case, we prove some new bounds for torsion anomalous points and we clarify the implications of several height bounds on the effective Mordell-Lang Conjecture. We also explicitly bound the Neron-Tate height of the rational points of a family of curves of increasing genus.

Related

• About the Proof of Lang's Height Conjecture
• Effective height bounds via Mordell Weil lattice symmetries
• Proof of Serge Lang's Heights Conjecture and an almost optimal Bound for the Torsion of Elliptic Curves
• A statistical view on the conjecture of Lang about the canonical height on elliptic curves
• Heights of Rational Points on Mordell Curves