Profinite properties of algebraically clean graphs of free groups

TL;DR

This paper establishes that algebraically clean graphs of free groups possess key residual and cohomological properties, including virtual residual $p$-finiteness and cohomological goodness, with applications to specific Artin groups.

Contribution

It proves that algebraically clean graphs of free groups are virtually residually $p$-finite and cohomologically $p$-complete, and that they are cohomologically good, extending understanding of their algebraic structure.

Findings

Graphs of free groups are virtually residually p-finite.

Graphs of free groups are cohomologically p-complete.

Graphs of free groups are cohomologically good.

Abstract

We prove that for every prime $p$ algebraically clean graphs of groups are virtually residually $p$-finite and cohomologically $p$-complete. We also prove that they are cohomologically good. We apply this to certain $2$-dimensional Artin groups.