Variations of the truncated Nevanlinna-Cartan's theorem in the context of function fields |
Natalia Garcia |
Universidad Católica de Chile |
Abstract: |
In 1996, Noguchi and Wang (independently) proved analogues of Nevanlinna-Cartan's Second Main Theorem with truncated counting functions for function fields. As in Cartan's theorem, the level of truncation was equal to the dimension of the ambient projective space. |
Using the theory of \[\omega\] -integral curves studied by Vojta, we prove variations of Noguchi-Wang's theorem with other truncations. In particular, we obtain a bound of the height of a non-constant morphism from a curve to the projective plane in terms of the number of intersections (without multiplicities) of its image with a divisor of a particular kind. This proves some new special cases of Vojta's conjecture with truncated counting functions in the context of function fields. |