In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and f -representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish ...

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes’ transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by ...