A note on the rational homological dimension of lattices in positive characteristic

Abstract

We show via ${\ell }^2$-homology that the rational homological dimension of a lattice in a product of simple simply connected Chevalley groups over global function fields is equal to the rational cohomological dimension and to the dimension of the associated Bruhat--Tits building.

4 pages

References in corpus (2)

• Lattices in a product of trees, hierarchically hyperbolic groups, and virtual torsion-freeness
• Graphs and complexes of lattices