Global field

Summary

A global field is either a number field or a global function field. A number field is a finite extension of $\Q$, and a global function field is a finite extension of $\F_q(t)$ for a finite field $\F_q$. The two kinds share much of their arithmetic: rings of integers, class groups, the product formula, adeles and class field theory. Their completions at places are the local fields.