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...

into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification...

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...

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...

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...

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...

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...

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...

name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can...

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...

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

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...

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...

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...

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...

(–, –) from K× × K× to the group of nth roots of unity in a local field K such as the fields of reals or p-adic numbers. It is related to reciprocity laws...

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...

might not. It might be local, or it might be nonlocal. However, "quantum fields do not exist as a point taken in isolation," so "local" does not mean literally...

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)...

of tools for computing the Galois cohomology of local fields. Let K be a non-archimedean local field, let Ks denote a separable closure of K, and let...

Naples. The Phlegraean Fields is monitored by the Vesuvius Observatory. It was declared a regional park in 2003. The Phlegraean Fields' largest known eruptions...

over local fields, or more generally, over ultrametric fields. In the original case, the ultrametric field of interest was essentially the field of formal...

their places such that the corresponding local fields are Witt equivalent. In particular, two number fields K and L are Witt equivalent if and only if...

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

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

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

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...