# Quasirationality and prounipotent crossed modules

## TL;DR

This paper investigates quasirational presentations of pro-p groups, including aspherical and one-relator cases, and addresses a variation of Serre's question using schematization techniques.

## Contribution

It introduces schematization of QR-presentations and provides new insights into the structure of one-relator pro-p groups, answering a variation of Serre's question.

## Key findings

- QR-presentations encompass aspherical and subpresentations
- Schematization offers new tools for analyzing pro-p groups
- Addresses Serre's question on one-relator pro-p groups

## Abstract

Quasirational presentations ($QR$-presentations) of (pro-$p$)groups are studied. Such presentations include, in particular, aspherical presentations of discrete groups and their subpresentations and pro-$p$-groups with a single defining relation. Using schematization of $QR$-presentations we answer a variation of J.-P. Serre's question on one-relator pro-$p$-groups.