论文标题
非特定品种和广义的lang-vojta猜想
Nonspecial varieties and Generalized Lang-Vojta conjectures
论文作者
论文摘要
我们构建了一个纤维的三倍$ x_m \ to（s，δ）$的家族，因此$ x_m $没有étale盖盖，它占主导地位，但它主导了一般类型的Orbifold $（s，Δ）$。在Campana之后，三倍$ x_m $称为\ emph {弱特殊}，但不是\ emph {special}。弱的猜想预测，在数字字段上定义的弱特殊变体具有潜在的密集的理性点。我们证明，如果$ m $足够大，那么三倍$ x_m $的行为与弱特殊性猜想的功能字段和分析类似物相矛盾。我们通过调整Ru和Vojta的最新方法来证明我们的结果。我们还对适合Campana计划的特殊基因座进行了一些已知猜想的概括，并证明了某些情况在功能领域上。
We construct a family of fibered threefolds $X_m \to (S , Δ)$ such that $X_m$ has no étale cover that dominates a variety of general type but it dominates the orbifold $(S,Δ)$ of general type. Following Campana, the threefolds $X_m$ are called \emph{weakly special} but not \emph{special}. The Weak Specialness Conjecture predicts that a weakly special variety defined over a number field has a potentially dense set of rational points. We prove that if $m$ is big enough the threefolds $X_m$ present behaviours that contradict the function field and analytic analogue of the Weak Specialness Conjecture. We prove our results by adapting the recent method of Ru and Vojta. We also formulate some generalizations of known conjectures on exceptional loci that fit into Campana's program and prove some cases over function fields.
