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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

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Formal étaleness along Henselian thickenings

Assume that $f:X\to Y$ is an étale map between smooth varieties and $(S,I)$ is a Henselian pair. Let $\alpha\in X(S/I)$. Can we say that the lifts of $\alpha$ to $X(S)$ are in bijection with the lifts …