The Arithmetic of Fields

Abstract

This is the report on the Oberwolfach workshop The Arithmetic of Fields, held in February 2006. Field Arithmetic (MSC 12E30) is a branch of mathematics concerned with studying the inner structure (orderings, valuations, arithmetic, diophantine properties) of fields and their algebraic extensions using Galois theory, algebraic geometry and number theory, partially in connection with model theoretical methods from mathematical logic.