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...

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...

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...

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...

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

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...

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...

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...

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...

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

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...

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...

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...

a local principal ideal domain, and not a field. R is a valuation ring with a value group isomorphic to the integers under addition. R is a local Dedekind...

in central Ipswich and spent much of her youth playing sport on the local fields there. Dakota attended Ipswich Girls' Grammar School throughout her upbringing...

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)...

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...

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...

Cambridge University Press. ISBN 9780511791260. Cassels, J.W.S. (1986). Local fields. London Mathematical Society Student Texts. Vol. 3. Cambridge: Cambridge...

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...

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...

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...

vector fields z n ∂ z {\displaystyle z^{n}\partial _{z}} . Strictly speaking, it is possible for a two-dimensional conformal field theory to be local (in...

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

Ghosts are necessary to keep gauge invariance in theories where the local fields exceed a number of physical degrees of freedom. If a given theory is...