Abstract: | We prove a sharper so-called Mordell-Lang plus Bogomolov type result for curves lying in the two-dimensional linear torus.
We mainly follow the approach of Rémond in (Comp Math 134:337–366, 2002), using Vojta and Mumford type inequalities. In the
special case we consider, we improve Rémond’s main result using a better Bogomolov property and an elementary arithmetic Bézout
theorem. |