An $abcd$ theorem over function fields and applications
摘要
We provide a lower bound for the number of distinct zeros of a sum 1 + u + v for two rational functions u, v, in term of the degree of u, v, which is sharp whenever u, v have few distinct zeros and poles compared to their degree. This sharpens the "abcd-theorem" of Brownawell-Masser and Voloch in some cases which are sufficient to obtain new finiteness results on diophantine equations over function fields. For instance, we show that the Fermat-type surface x a + y a + z c = 1 contains only finitely many rational or elliptic curves, provided a 10 4 and c 2; this provides special cases of a known conjecture of Bogomolov.
引用本文（GB/T 7714）
Pietro Corvaja, Umberto Zannier. An $abcd$ theorem over function fields and applications[J]. Bulletin de la Société mathématique de France, 2011.
引文网络
本站仅收录题录与摘要供学习参考，全文版权归属出版方；如有侵权请联系我们删除。