We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two explicit versions of the inverse function theorem, the first via general distribution and separation inequalities that may be of independent interest, the second via a careful implementation of classical Newton iteration.

中文翻译：

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算术几何中的分布关系和逆函数定理

我们研究代数和算术几何中的算术分布关系和逆函数定理，重点是可以在变体和图族之间统一应用的版本。特别地，我们证明了逆函数定理的两个显式形式，第一个通过可能具有独立利益的一般分布和分离不等式，第二个通过经典牛顿迭代的仔细实现。