Semidualities from products of trees

Abstract

Let $K$ be a global function field of characteristic $p$, and let $\Gamma$ be a finite-index subgroup of an arithmetic group defined with respect to $K$ and such that any torsion element of $\Gamma$ is a $p$-torsion element. We define semiduality groups, and we show that $\Gamma$ is a $\mathbb{Z}[1/p]$-semiduality group if $\Gamma$ acts as a lattice on a product of trees. We also give other examples of semiduality groups, including lamplighter groups, Diestel-Leader groups, and countable sums of finite groups.

40 pages, v2: naturality of `semiduality' homomorphisms added, equivalent characterization of semiduality added in Section 2, various other revisions

References in corpus (2)

• Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem
• Bounding the homological finiteness length