VIC-modules over noncommutative rings

Abstract

For a finite ring $R$, not necessarily commutative, we prove that the category of $\text{VIC}(R)$-modules over a left Noetherian ring $\mathbf{k}$ is locally Noetherian, generalizing a theorem of the authors that dealt with commutative $R$. As an application, we prove a very general twisted homology stability for ${\text{GL}}_n(R)$ with $R$ a finite noncommutative ring.

23 pages, minor revision. To appear in Selecta Math

References in corpus (1)

• Stability in the homology of unipotent groups