The dualizing module and top-dimensional cohomology group of ${\text{GL}}_n(\mathcal{O})$

Andrew Putman, Daniel Studenmund

For a number ring $\mathcal{O}$, Borel and Serre proved that ${\text{SL}}_n(\mathcal{O})$ is a virtual duality group whose dualizing module is the Steinberg module. They also proved…