We prove that the fibered power conjecture of Caporaso et al. (Conjecture H,[CHM, Sec. 6]together with Lang's conjecture implies the uniformity of rational points on varieties ofgeneral type, as predicted in [CHM]; a few applications on the arithmeticand geometry of curves are stated. In an opposite direction, we give counterexamples to some analogous results inpositive characteristic. We show that curves that change genus can havearbitrarily many rational points; and that curves over ar{F}p(t) can have arbitrarilymany Frobenius orbits of non-constant points.
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机译：我们证明了Caporaso等人的光纤功率猜想。 （[H，[CHM，Sec。6]猜想与Lang的猜想一起暗示了一般类型的有理点的一致性，如[CHM]所预测;陈述了曲线在算术和几何上的一些应用。相反，我们给出了一些类似结果的正特征的反例，表明改变类的曲线可以具有任意多个有理点;在 bar {F} p（t）上的曲线可以具有任意多个非恒定点的Frobenius轨道。
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