The same statement holds even more generally for all global fields.

Therefore, both types of field are called global fields.

F is a global field, such as the field of rational numbers.

In mathematics, the term global field refers to either of the following:

However, general class field theory used different concepts and its constructions work over every global field.

This idea is more precisely encoded in the theory that global fields should all be treated on the same basis.

He is as much at home in the world of music as in the global field that contemporary architecture has become.

(An example of this situation is the adele ring of a global field.

G is a vector space over the adeles of a number field (or global field).

The case of a global field K is addressed by the global class field theory.

This approach was further developed by Langlands, for general reductive algebraic groups over global fields.

Local fields arise naturally in number theory as completions of global fields.

For global fields the combined work of several authors shows that this Whitehead group is always trivial .

In mathematics, an infrastructure is a group-like structure appearing in global fields.

This choice, seeming somewhat arbitrary, appears in a natural way when one tries to obtain infrastructures from global fields.

It is used to encode ramification data for abelian extensions of a global field.

It was introduced by for local fields and by for global fields.

The accuracy of global field models depends on the worldwide network of magnetic observatories.

Part 2: The generation of global fields of terrestrial biophysical parameters from satellite data.

In the context of this analogy, number fields and function fields are usually called global fields.

The Artin conductor appears in the conductor-discriminant formula for the discriminant of a global field.

The study of Galois modules for extensions of local or global fields is an important tool in number theory.

For example, global fields are Hilbertian.

One natural development in number theory is to understand and construct nonabelian class field theories which provide information about general Galois extensions of global fields.