Small points on constant arithmetic surfaces
The paper under review considers Arakelov theory. That is we start with a regular semistable curve X over the integers of a number-field, and can define an intersection theory for Arakelov divisors on X very much as for algebraic surfaces. Such a surface, of genus \(g\geq 2,\) is called constant if its dualising sheaf \(\omega_ X\) satisfies \(\omega^ 2_ X=0\). It is known that always \(\omega^ 2_ X\geq 0\), and there is some evidence for the conjecture that constant arithmetic surfaces do not exist. Anyway in the present paper the author first constructs sections of suitably bounded norm in \(\Gamma (X,\omega^ n)\), and then uses them to construct an infinite sequence of algebraic points whose Néron-Tate heights converge to zero.
scientific article; zbMATH DE number 4200374