Homological growth of Artin kernels in positive characteristic

Sam P. Fisher, Sam Hughes, Ian J. Leary

Published 2022-12-06Version 1

We prove an analogue of the L\"uck Approximation Theorem in positive characteristic for certain residually finite rationally soluble groups including right-angled Artin groups and Bestvina--Brady groups. Specifically, we prove that the mod $p$ homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. We also consider a number of applications to fibring, amenable category, and minimal volume entropy.