Work

A proper arithmetic surface with infinite étale fundamental group

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.05972

Author: Chenal, Pablo

Institutions: Université Paris-Saclay, École Normale Supérieure - PSL, Laboratoire de Mathématiques d'Orsay, Département de mathématiques et applications

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220660578

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