  This work is a dissertation thesis written at the WWU Muenster (Germany),
supervised by Prof. Dr. Raimar Wulkenhaar. We present an approach to adelic
physics based on the language of algebraic spaces. Relative algebraic spaces X
over a base S are considered as fundamental objects which describe space-time.
This yields a formulation of general relativity which is covariant with respect
to changes of the chosen domain of numbers S. With regard to adelic physics the
choice of S as an excellent Dedekind scheme is of interest (because this way
also the finite prime spots, i.e. the p-adic degrees of freedom are taken into
account). In this arithmetic case, it turns out that X is a Neron model. This
enables us to make concrete statements concerning the structure of the
space-time described by X. Furthermore, some solutions of the arithmetic
Einstein equations are presented. In a next step, Yang-Mills gauge fields are
incorporated.
