Explore: Class Field Theory

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions

local class field theory (LCFT), introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which

In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification

rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics

which is finite, is called the class number of K {\displaystyle K} . The theory extends to Dedekind domains and their fields of fractions, for which the

In mathematics, non-abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and

number theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K. Its degree over K equals the class number

geometric class field theory is an extension of class field theory to higher-dimensional geometrical objects: much the same way as class field theory describes

module theory of ideal class groups, initiated by Kenkichi Iwasawa (1959) (岩澤 健吉), as part of the theory of cyclotomic fields. In the early 1970s, Barry

In mathematics, class field theory is the study of abelian extensions of local and global fields. 1801 Carl Friedrich Gauss proves the law of quadratic