Global Field

(Algebraic Number Theory)

Tech

sciences
Algebraic Number Theory
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What is Global field?

In mathematics, a global field is a field that is either: * an algebraic number field, i.e., a finite extension of Q, or * a global function field, i.e., the function field of an algebraic curve over a finite field, equivalently, a finite extension of Fq(T), the field of rational functions in one variable over the finite field with q elements. An axiomatic characterization of these fields via valuation theory was given by Emil Artin and in the 1940s.

Technology Types

algebraic curvealgebraic number theoryfield (mathematics

Synonyms

Global function fieldProduct formula

Tech Info


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