fields, the fields of p-adic numbers for positive prime integer p, were introduced by Kurt Hensel at the end of the 19th century. Every local field is...

extensions of "local" (i.e., complete for a discrete valuation) fields with finite residue field.[dubious – discuss] Part I, Local Fields (Basic Facts):...

Local field potentials (LFP) are transient electrical signals generated in nerves and other tissues by the summed and synchronous electrical activity...

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...

known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational...

multi-dimensional local fields. On the usual local fields (typically completions of number fields or the quotient fields of local rings of algebraic curves) there...

finite residue field. Let L / K {\displaystyle L/K} be a finite Galois extension of nonarchimedean local fields with finite residue fields ℓ / k {\displaystyle...

extensions of a valuation of a field K to an extension field of K. This generalizes the notions in algebraic number theory, local fields, and Dedekind domains...

theory of rank one valued fields and normed spaces over rank one valued fields as follows. Let K {\displaystyle K} be a field endowed with an absolute...

groups over local fields (with different subcases corresponding to archimedean local fields, p-adic local fields, and completions of function fields) Automorphic...

such that their completions give a Galois field extension K w / k v {\displaystyle K_{w}/k_{v}} of local fields, there is an induced action of the Galois...

at a local level first, that is to say, by looking at the corresponding local fields. For number fields K {\displaystyle K} , the local fields are the...

Lusztig (1995) classified the unipotent characters over non-archimedean local fields. Vogan (1987) discusses several different possible definitions of unipotent...

of algebraic number fields in the p-adic context. One of the useful structure theorems for vector spaces over locally compact fields is that the finite...

in some cases, for example over the real or p-adic fields, and thereby over number fields via local-global principles. Abelian varieties are connected...

the computations of K-theory of global fields (such as number fields and function fields), as well as local fields (such as p-adic numbers). Suslin (1983)...

global field is one of two types of fields (the other one is local fields) that are characterized using valuations. There are two kinds of global fields: Algebraic...

football field crushes other local fields". WLEX-TV. Retrieved August 25, 2024. Rosenthal, Gregg (March 22, 2011). "There will be no blue NFL fields". Pro...

Look up Elysian Fields in Wiktionary, the free dictionary. The Elysian Fields, also called Elysium, are the final resting place of the souls of the heroic...

be local, or it might be nonlocal. Noether fields are often composite fields and they are local. In the generalized LSZ formalism, composite fields, which...

algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring...

fields are not extendable to the general case of algebraic number fields, and different conceptual principles are in use in the general class field theory...

every field extension F/k. (see below) Otherwise, k is called imperfect. In particular, all fields of characteristic zero and all finite fields are perfect...

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

representations of general linear groups over local fields. The local Langlands conjecture for GL2 of a local field says that there is a (unique) bijection...

spectrometer's applied magnetic field B 0 {\displaystyle B_{0}} but also to any local magnetic fields of atoms or molecules. The effective field B eff {\displaystyle...

for much of modern quantum field theory, including a variational approach, and the equations of motion for quantum fields. He developed the first electroweak...

of the symplectic group over R; it has analogues over other local fields, finite fields, and adele rings. The symplectic group is a classical group defined...

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...

Proceedings of a Conference on Local Fields, Springer-Verlag, pp. 158–183, MR 0231827 Artin, Emil; Tate, John (2009) [1967], Class field theory, AMS Chelsea Publishing...