A NOTE ON p-ADIC SIMPLICIAL VOLUMES

We define and study generalizations of simplicial volume over arbitrary seminormed rings with a focus on p -adic simplicial volumes. We investigate the dependence on the prime and establish homology bounds in terms of p -adic simplicial volumes. As the main examples, we compute the weightless and p -adic simplicial volumes of surfaces. This is based on an alternative way to calculate classical simplicial volume of surfaces without hyperbolic...