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

class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and...

an Archimedean local field, in the second case, one calls it a non-Archimedean local field. Local fields arise naturally in number theory as completions...

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...

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

Serre, Jean-Pierre (1967), "VI. Local class field theory", in Cassels, J.W.S.; Fröhlich, A. (eds.), Algebraic number theory. Proceedings of an instructional...

Class field theory Abelian extension Kronecker–Weber theorem Hilbert class field Takagi existence theorem Hasse norm theorem Artin reciprocity Local class...

and local class field theory. The book's end goal is to present local class field theory from the cohomological point of view. In this book, a Local field...

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...

algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine...

local field has many features similar to those of the one-dimensional local class field theory. Higher local class field theory is compatible with class field...

In number theory, more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension...

Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic...

to organize the various Galois groups and modules that appear in class field theory. A formation is a topological group G together with a topological...

thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups. The local Langlands conjectures for GL1(K)...

quasi-finite field is a generalisation of a finite field. Standard local class field theory usually deals with complete valued fields whose residue field is finite...

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...

names of the Hilbert class field and of the Hilbert symbol of local class field theory. Results were mostly proved by 1930, after work by Teiji Takagi...

a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations...

idea of passing from local data to global ones proves fruitful in class field theory, for example, where local class field theory is used to obtain global...

symbol on local fields and higher local field, higher class field theory, p-class field theory, arithmetic noncommutative local class field theory. He coauthored...

law introduced by Lubin and Tate (1965) to isolate the local field part of the classical theory of complex multiplication of elliptic functions. In particular...

Project Hazewinkel, Michiel (1989). "Review of Class field theory by Jürgen Neukirch and Local class field theory by Kenkichi Iwasawa". Bull. Amer. Math. Soc...

In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes...

local class field theory" (PDF). Mathematical Journal of Okayama University. 3 (1): 5–10. 1953. ISSN 0030-1566. f. g. Schilling, O. (1961). "On local...

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory and the principle of relativity with ideas behind...

algebraic K-theory. With Jonathan Lubin, he recast local class field theory by the use of formal groups, creating the Lubin–Tate local theory of complex...

1927; 1930), is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long...

Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for...

Brauer class of algebras over a field. The concept is named after Helmut Hasse. The invariant plays a role in local class field theory. Let K be a local field...