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arXiv · 2203.11750

Variants of the de Jong fundamental group

Piotr Achinger·Marcin Lara·Alex Youcis
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Abstract

For a rigid space $X$, we answer two questions of de Jong about the category $\mathbf{Cov}^\mathrm{adm}_X$ of coverings which are locally in the admissible topology on $X$ the disjoint union of finite etale coverings: we show that this class is different from the one used by de Jong, but still gives a tame infinite Galois category. In addition, we prove that the objects of $\mathbf{Cov}^\mathrm{et}_X$ (with the analogous definition) correspond precisely to locally constant sheaves for the pro-etale topology defined by Scholze.

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Piotr Achinger, Marcin Lara, Alex Youcis. 2022-03-22. Variants of the de Jong fundamental group. https://arxiv.org/abs/2203.11750

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