# Aspherical neighborhoods on arithmetic surfaces: the local case

## TL;DR

This paper investigates the local geometric structure of arithmetic surfaces over local rings of integers, focusing on the existence of neighborhoods with specific homotopy types related to finite group classes.

## Contribution

It introduces criteria for neighborhoods on arithmetic surfaces to have $K(\pi,1)$-type homotopy types in the context of a full class of finite groups.

## Key findings

- Existence of neighborhoods with $K(\pi,1)$-type homotopy types under certain conditions
- Characterization of local geometric points with such neighborhoods
- Insights into the étale homotopy types of arithmetic surfaces

## Abstract

On arithmetic surfaces over local rings of integers we examine whether any geometric point has a basis of \'etale neighborhoods whose $\mathfrak{c}$-completed \'etale homotopy types are of type $K(\pi,1)$ for a given full class~$\mathfrak{c}$ of finite groups.

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Source: https://tomesphere.com/paper/1702.05736