Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall.
We prove a new lower bound for the height of points on a subvariety of a multiplicative torus, which lie outside the union of torsion subvarieties of . Although lower bounds for the heights of these points where already known (decreasing multi-exponential function of the degree for Scmhidt and Bombieri–Zannier, [Sch], [Bo-Za], and inverse monomial in the degree by the second author of this note and P. Philippon, [Da-Phi]), our method provesup to an the sharpest conjectures that can be formulated....
In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces , nowadays called Faltings’s delta function and here denoted by . For a given compact Riemann surface of genus , the invariant is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space of genus curves determined by to its boundary . In this paper we begin by revisiting a formula derived in [14],...