Affiliation:
1. Department of Mathematics, Brown University , Providence, RI 02912, USA
Abstract
Abstract
In this paper, we prove a uniform version of Poonen’s “Mordell-Lang Plus Bogomolov” theorem [ 12], based on Vojta’s method. Our main contribution is to generalize Rèmond’s work on the large points in order to allow an extra $\epsilon $-neighborhood in the canonical height topology. The part on small points follows from [ 8].
Publisher
Oxford University Press (OUP)
Reference20 articles.
1. Point of finite order on an abelian variety;Bogomolov;Mathematics of the USSR-Izvestiya,1981
2. Chapter VII: Arakelov geometry, heights, equidistribution, and the Bogomolov conjecture;Chambert-Loir,2021
3. Minorations des hauteurs normalisées des sous-variétés des puissances des courbes elliptiques;David;Int. Math. Res. Pap. IMRP,2007
4. Uniformity in Mordell-Lang for curves;Dimitrov;Ann. of Math. (2),2021
5. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern;Faltings;Invent. Math.,1983