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arXiv · 2610.05972

A proper arithmetic surface with infinite étale fundamental group

Pablo Chenal
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Abstract

We give an example of a proper, regular, integral arithmetic surface over $\mathrm{Spec}\ \Z$ endowed with a section, and whose étale fundamental group admits an infinite pro-$2$ quotient. The construction is a geometric analog of the Golod--Shafarevich towers for rings of integers of number fields.

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Pablo Chenal. 2026-10-05. A proper arithmetic surface with infinite étale fundamental group. https://arxiv.org/abs/2610.05972

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