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

Arithmetic gravity and Yang-Mills theory: An approach to adelic physics via algebraic spaces