Foundations of the Theory of Algebraic Function Fields

In this chapter we introduce the basic definitions and results of the theory of algebraic function fields: valuations, places, divisors, the genus of a function field, adeles, Weil differentials and the Riemann-Roch Theorem.

It is only in later chapters that we will assume that K has specific properties (for example, that K is a finite field — the case which is of particular interest to coding theory).