Local class field theory information

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...

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...

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...

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)...

an area of the body Local class field theory, the study of abelian extensions of local fields Local field, a special type of field that is a locally compact...

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

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...

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

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

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...

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics...

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...

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...

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

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...

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...

reciprocity laws, and can be defined in terms of the Artin symbol of local class field theory. The Hilbert symbol was introduced by David Hilbert (1897, sections...

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...

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...

cohomology, and local class field theory. The book's end goal is to present local class field theory from the cohomological point of view. This theory concerns...

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

group of K and its study leads to local class field theory. For global class field theory, the union of the idele class groups of all finite separable extensions...

field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory uses...

modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F, its Weil group is generally denoted WF...