Lang-Vojta conjecture over function fields for surfaces dominating $${ {\mathbb {G}}}_m^2$$
Lang-Vojta conjecture over function fields for surfaces dominating $${ {\mathbb {G}}}_m^2$$
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主导表面函数场的 Lang-Vojta 猜想 $${ {mathbb {G}}}_m^2$$
DOI：
10.1007/s40879-021-00502-8
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发表时间：
2021
影响因子：
0.6
通讯作者：
Capuano L
中科院分区：
文献类型：
--
作者：
Capuano L
我们证明了函数域上log一般曲面的Lang-Vojta猜想的非分裂情况。这扩展了Corvaja和Zannier （J Differ Geom 93(3): 355-377, 2013）的结果，其中在分裂情况下证明了猜想，以及Corvaja和Zannier (J Algebr Geom 17(2): 295-333, 2008), Turchet （Trans Amer Math Soc 369(12): 8537-8558, 2017）在四次和三分量除数补的情况下获得的结果。我们遵循Corvaja和Zannier开发的策略，明确所有涉及的常数。
We prove the nonsplit case of the Lang–Vojta conjecture over function fields for surfaces of log general type that are ramified covers of. This extends the results of Corvaja and Zannier (J Differ Geom 93(3):355–377, 2013), where the conjecture was proved in the split case, and the results of Corvaja and Zannier (J Algebr Geom 17(2):295–333, 2008), Turchet (Trans Amer Math Soc 369(12):8537–8558, 2017) that were obtained in the case of the complement of a degree four and three component divisor in. We follow the strategy developed by Corvaja and Zannier and make explicit all the constants involved.