Search results

...<math>N_{L/K} </math> is the [[field norm]]. One of the main theorems in [[local class field theory]] states that the norm groups in <math>K^\times</math> a ...

...ty theorem]] for [[cohomology]] of [[module (mathematics)|modules]] over [[local ring]]s, analogous to [[Serre duality]] of [[coherent sheaf|coherent sheave Suppose that ''R'' is a [[Cohen–Macaulay ring|Cohen–Macaulay]] local ring of dimension ''d'' with maximal ideal ''m'' and residue field ''k''&nb ...

...''K'', for ''p'' a finite or infinite place of ''K'', and is equal to the local Hilbert symbol in the completion of ''K'' at the place ''p''. ...'', where the roots of unity can be identified with elements of the Galois group. ...

...d analysis can be carried out with the aid of tools such as [[ramification group]]s. In this article, a local field is non-archimedean and has finite [[residue field]]. ...

...ssociated to any [[conformal manifold]], at least locally. Intuitively, a local twistor is an association of a [[twistor space]] to each point of space-tim ...ntation, the [[spin representation]], and the [[associated bundle]] is the local twistor bundle. ...

...of the [[absolute Galois group]] ''G_K'' of a [[non-archimedean local field]] ''K''. ...is group of ''K'', and let ''Hⁱ''(''K'',&nbsp;''M'') denote the group cohomology of ''G_K'' with coefficients in ''M''. Since the [[coh ...

...eneralizes a [[group scheme]], which is a scheme whose sets of points have group structures in a compatible way. ...roup algebraic-space''', an algebraic-space analog of a group scheme, is a group-stack. ...

...pe''' or '''even type''' or of '''even characteristic''' if it resembles a group of Lie type over a [[field (mathematics)|field]] of [[Characteristic (algeb ...lassification of finite simple groups]], there is a major division between group of characteristic 2 type, where involutions resemble unipotent elements, an ...

...f ''GL''₂ over a [[local field]] on a space of functions on the local field. ...he [[algebraic group]] ''GL''₂ and '''F''' is a non-Archimedean local field, ...

...lity for Galois modules for the absolute Galois group of a non-archimedean local field}} ...s the [[Tate twist]] of usual linear dual. This new dual is called the ('''local''') '''Tate dual'''. ...

...ed in terms of their "chromatic levels"; i.e., the heights of the [[formal group]]s that define the theories via the [[Landweber exact functor theorem]]. Ty ...of the chromatic tower (defined below) of a finite [[local spectrum|''p''-local spectrum]] <math>X</math> is <math>X</math> itself. The theorem was proved ...

In [[algebra]], given an [[algebraic group]] ''G'', a [[group representation|''G''-module]] ''M'' and a ''G''-algebra ''A'', all over a [ *[[Local cohomology]] ...

In image [[Noise reduction]], '''local pixel grouping''' is the algorithm to remove noise from images using [[prin ...r, techniques such as smoothing filters and many other algorithms may lose local structure of image while denoising the image.<ref>{{Cite journal | doi = 10 ...

...y in [[algebraic K-theory|algebraic ''K''-theory]], the '''algebraic ''K''-group of a field''' is important to compute. For a finite field, the complete cal the [[multiplicative group]] of ''F''.<ref>{{harvnb|Weibel|2013|loc=Ch. III, Example 1.1.2.}}</ref> ...

...]] over a complete Noetherian [[local ring]]. In the special case when the local ring has a field{{clarify|reason=As a subfield? As a module?|date=May 2014} Suppose that ''R'' is a Noetherian complete local ring with residue field ''k'', and choose ''E'' to be an [[injective hull]] ...

...concept is named after [[Helmut Hasse]]. The invariant plays a role in [[local class field theory]]. ==Local fields== ...

...to define the [[Kirillov model]] of a representation of the general linear group. ...of {{mvar|k}} is a mirabolic subgroup of the 2-dimensional general linear group. ...

=== Local fields === ...te extensions <math>K/\mathbb{Q}_p</math>. Each of these are examples of [[local field]]s. Note the algebraic closure <math>\overline{\mathbb{Q}}_p</math> a ...

...y]] of ''E'', or de Rham cohomology with coefficients '''twisted''' by the local coefficient system ''E''. ...parallel vector fields are constant in the first case, and proportional to local determinations of the [[Square root#Square roots of negative and complex nu ...

...al]] field of infinite [[group theory]], the '''Nottingham group''' is the group ''J''('''F'''_''p'') or ''N''('''F'''_''p'') consistin with coefficients in '''F'''_''p''. The group multiplication is given by formal composition also called substitution. Tha ...