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...
11 KB (1,661 words) - 20:27, 2 July 2025
into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification...
4 KB (308 words) - 03:57, 31 May 2025
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...
8 KB (967 words) - 04:33, 27 May 2025
Local field potentials (LFP) are transient electrical signals generated in nerves and other tissues by the summed and synchronous electrical activity...
11 KB (1,374 words) - 04:56, 25 May 2025
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...
86 KB (10,330 words) - 20:24, 2 July 2025
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...
4 KB (371 words) - 18:34, 6 March 2025
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...
11 KB (1,381 words) - 01:39, 14 July 2024
Langlands program (section Local Langlands conjectures)
groups over local fields (with different subcases corresponding to archimedean local fields, p-adic local fields, and completions of function fields) Automorphic...
21 KB (2,327 words) - 12:38, 4 July 2025
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...
20 KB (2,041 words) - 03:07, 11 May 2025
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...
90 KB (4,942 words) - 13:45, 26 June 2025
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...
52 KB (8,509 words) - 03:55, 10 July 2025
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...
16 KB (2,203 words) - 02:36, 11 May 2025
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...
8 KB (1,227 words) - 08:09, 9 January 2025
Archimedean property (redirect from Archimedean field)
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...
16 KB (2,387 words) - 23:59, 30 June 2025
Ramification (mathematics) (section In local fields)
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...
8 KB (1,116 words) - 01:50, 18 April 2025
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...
8 KB (1,054 words) - 10:24, 23 April 2025
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...
5 KB (758 words) - 21:05, 16 June 2025
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...
18 KB (3,236 words) - 19:53, 28 June 2025
Hilbert symbol (category Class field theory)
(–, –) 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...
11 KB (1,645 words) - 03:54, 4 May 2025
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...
4 KB (580 words) - 15:09, 19 September 2021
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...
2 KB (332 words) - 23:26, 24 May 2024
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...
2 KB (180 words) - 06:32, 27 June 2025
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)...
3 KB (409 words) - 01:20, 9 March 2025
Witt group (redirect from Reciprocity equivalence of fields)
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...
21 KB (3,163 words) - 18:06, 2 May 2025
over local fields, or more generally, over ultrametric fields. In the original case, the ultrametric field of interest was essentially the field of formal...
14 KB (2,413 words) - 01:21, 10 May 2025
Naples. The Phlegraean Fields is monitored by the Vesuvius Observatory. It was declared a regional park in 2003. The Phlegraean Fields' largest known eruptions...
43 KB (4,485 words) - 03:11, 3 July 2025
more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives...
14 KB (2,553 words) - 23:20, 6 July 2025
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...
16 KB (2,244 words) - 15:28, 15 May 2025
symbol on local fields and higher local field, higher class field theory, p-class field theory, arithmetic noncommutative local class field theory. He...
12 KB (1,174 words) - 11:24, 6 July 2025
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...
9 KB (1,174 words) - 18:12, 2 July 2025