An effective Schmidt's subspace theorem over function fields
In the paper under review a version of the effective Schmidt's subspace theorem over function fields is dealt with. Let \(K\) be a function field of a nonsingular variety over an algebraically closed field of characteristic zero. Then the author proves an effective Schmidt's subspace theorem for \(\mathbb{P}^N(K)\). It is noticed that Schmidt's subspace theorem over function fields corresponds to the second main theorem of Nevanlinna-Cartan for moving targets. In the proof of the main result, she first proves the Nevanlinna-Cartan second main theorem over function fields of non-singular varieties with moving targets. To ensure the effectiveness, she next uses \textit{P. Vojta's} methods [Am. J. Math. 111, No. 3, 489--518 (1989; Zbl 0662.14002)].
scientific article; zbMATH DE number 2078074