AI & ChatGPT searches , social queries for LOCAL FIELD
Search references for LOCAL FIELD. Phrases containing LOCAL FIELD
See searches and references containing LOCAL FIELD!
Search references for LOCAL FIELD. Phrases containing LOCAL FIELD
See searches and references containing LOCAL FIELD!LOCAL FIELD
Locally compact topological field
In mathematics, a local field is a locally compact Hausdorff non-discrete topological field. Local fields find many applications in algebraic number theory
Local_field
Transient electrical signals
Local field potentials (LFP) are transient electrical signals generated in nerves and other tissues by the summed and synchronous electrical activity
Local_field_potential
Book by Jean-Pierre Serre
into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification
Local_Fields
local class field theory (LCFT), introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which
Local_class_field_theory
Discrete valuation field
(-dimensional) local field is an important example of a complete discrete valuation field. Such fields are also sometimes called multi-dimensional local fields. On
Higher_local_field
of local fields where a more detailed analysis can be carried out with the aid of tools such as ramification groups. In this article, a local field is
Finite extensions of local fields
Finite_extensions_of_local_fields
Algebraic structure with addition, multiplication, and division
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
Field_(mathematics)
Conjectures connecting number theory and geometry
groups over local fields (with different subcases corresponding to archimedean local fields, p-adic local fields, and completions of function fields) Automorphic
Langlands_program
Mathematical conjectures in class field theory
representations of a reductive algebraic group G {\displaystyle G} over a local field F {\displaystyle F} , and representations of the Langlands group of F
Local_Langlands_conjectures
Branch of algebraic number theory concerned with abelian extensions
class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global
Class_field_theory
Brainwaves, repetitive patterns of neural activity in the central nervous system
the central nervous system at all levels, and include spike trains, local field potentials and large-scale oscillations which can be measured by electroencephalography
Neural_oscillation
Public school district in Ohio, U.S.
The Field Local School District is a public school district based in Brimfield, Ohio, United States, that serves Brimfield and Suffield Townships, and
Field_Local_School_District
Mathematical concept
In mathematics, a global field is one of two types of fields (the other one is local fields) that are characterized using valuations, or absolute values
Global_field
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
Quasi-finite_field
Function used in local class field theory related to reciprocity laws
of global fields rather than for the larger local fields. The Hilbert symbol has been generalized to higher local fields. Over a local field K {\displaystyle
Hilbert_symbol
a quadratic field extension. Complete field Locally compact group – Type of topological group in mathematics Ramification of local fields Topological
Locally_compact_field
notions is motivated by the local–global principle that relates properties of a number field with properties of all its local fields. The definition of an order
Order_(ring_theory)
In the mathematical field of Galois cohomology, the local Euler characteristic formula is a result due to John Tate that computes the Euler characteristic
Local Euler characteristic formula
Local_Euler_characteristic_formula
Linear representation in mathematics
linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is analogous to the 1-dimensional
Steinberg_representation
Quantum field theory enjoying conformal symmetry
infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important
Conformal_field_theory
Emission of electrons induced by an electrostatic field
Field electron emission, also known as field-induced electron emission, field emission (FE) and electron field emission, is the emission of electrons from
Field_electron_emission
Mathematical formal group law
formal group law introduced by Lubin and Tate (1965) to isolate the local field part of the classical theory of complex multiplication of elliptic functions
Lubin–Tate_formal_group_law
Duality for Galois modules for the absolute Galois group of a non-archimedean local field
cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean local field. It is
Local_Tate_duality
Filtration of the Galois group of a local field extension
more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives
Ramification_group
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
Conductor (class field theory)
Conductor_(class_field_theory)
Finite extension of the rationals
mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle
Algebraic_number_field
MRI, the local field δ B {\displaystyle \delta B} induced by non-ferromagnetic biomaterial susceptibility along the main polarization B0 field is the convolution
Quantitative susceptibility mapping
Quantitative_susceptibility_mapping
Tendency of matter subjected to an electric field to acquire an electric dipole moment
moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. Note that the local electric field seen by a molecule
Polarizability
A high-field domain is a band of elevated field orthogonal to the equi-current lines, and seen in photoconductive CdS and monochromatic light at the band
High-field_domain
Theorem in abstract algebra
fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups.[clarification needed]
Fundamental lemma (Langlands program)
Fundamental_lemma_(Langlands_program)
number or ideal associated to a character of a Galois group of a local or global field, introduced by Emil Artin as an expression appearing in the functional
Artin_conductor
Algebra term
to the group ring (Z/2Z)[F*/F*2] if q ≡ 1 mod 4. The Witt ring of a local field with maximal ideal of norm congruent to 1 modulo 4 is isomorphic to the
Witt_group
Used to compare mixed characteristic situations with purely finite characteristic ones
such as local fields of characteristic zero which have residue fields of characteristic prime p. A perfectoid field is a complete topological field K whose
Perfectoid_space
Field-equations in general relativity
as implying local energy–momentum conservation, the EFE reduce to Newton's law of gravitation in the limit of a weak gravitational field and velocities
Einstein_field_equations
Concept in ring theory
not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where R {\displaystyle R} is a commutative local ring. The
Azumaya_algebra
algebraic number field or local field, introduced by John Tate (1962) and Georges Poitou (1967). For a p-adic local field k {\displaystyle k} , local Tate duality
Tate_duality
Mathematical property of algebraic structures
axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are
Archimedean_property
Mathematical object
usual notion of admissible representation when the local field is non-Archimedean. When the local field is Archimedean, admissible representation instead
Gelfand_pair
Elementary function in mathematics
with a representation ρ {\displaystyle \rho } of the Weil group of a local field. The functional equation L ( ρ , s ) = ε ( ρ , s ) L ( ρ v , 1 − s )
Langlands–Deligne local constant
Langlands–Deligne_local_constant
On the character of the representation of a reductive algebraic group
L2(G(F)), for G a reductive algebraic group over a local field F. Arthur, James (1991), "A local trace formula", Publications Mathématiques de l'IHÉS
Local_trace_formula
Competitive event for dogs
tests. In the United Kingdom they are called field tests and are most frequently run by gun clubs or local field sports organisations. In the United States
Field_trial
Topics referred to by the same term
Oberlin, Ohio Field (sculpture), by Anthony Gormley Field department, the division of a political campaign tasked with organizing local volunteers and
Field
Field theory is the branch of algebra that studies fields
Formally real field Real closed field Global field A number field or a function field of one variable over a finite field. Local field A completion of
Glossary_of_field_theory
Russian mathematician
symbol on local fields and higher local field, higher class field theory, p-class field theory, arithmetic noncommutative local class field theory. He
Ivan_Fesenko
the finite field case and the archimedean local field case, but the remaining cases are more difficult. Most of the hard work of class field theory consists
Class_formation
Division of the U.S. Federal Bureau of Investigation
counterterrorism field operations organized into squads, the number of which varies according to the amount and diversity of activity in the local field office's
FBI_Counterterrorism_Division
Axiomatic approach to quantum field theory
Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework
Algebraic quantum field theory
Algebraic_quantum_field_theory
Map raising elements to the pth power, in characteristic p
of local fields, with ring of integers OK of K such that the residue field, the integers of K modulo their unique maximal ideal φ, is a finite field of
Frobenius_endomorphism
Vast void adjacent to the Local Group
The Local Void is a vast, empty region of space, lying adjacent to the Local Group. Discovered by Brent Tully and Rick Fisher in 1987, the Local Void is
Local_Void
Abelian group related to division algebras
Let K be a non-Archimedean local field, meaning that K is complete under a discrete valuation with finite residue field. Then Br K is isomorphic to Q/Z
Brauer_group
Physical theory with fields invariant under the action of local "gauge" Lie groups
theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according
Gauge_theory
In mathematics, class field theory is the study of abelian extensions of local and global fields. 1801 Carl Friedrich Gauss proves the law of quadratic
Timeline of class field theory
Timeline_of_class_field_theory
Process for promoting integrated pest management
treated plots. An FFS often includes several additional field studies depending on local field problems. Between 25 and 30 farmers participate in a FFS
Farmer_field_school
Albert form is isotropic. The field F is linked if any two quaternion algebras over F are linked. Every global and local field is linked since all quadratic
Linked_field
Mathematics award
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians (ICM) of
Fields_Medal
local fields I". Amer. J. Math. 87 (3): 605–630. doi:10.2307/2373065. JSTOR 2373065. Zbl 0136.32805. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic
Quasi-algebraically closed field
Quasi-algebraically_closed_field
Quantum field that enables consistent quantization
ghosts are introduced to maintain gauge invariance in theories where the local field components exceeds the number of physical degrees of freedom. Ghosts
Ghost_(physics)
of a reductive dual pair. The local theta correspondence relates irreducible admissible representations over a local field, while the global theta correspondence
Theta_correspondence
Solving integer equations from all modular solutions
when can local solutions be joined to form a global solution? One can ask this for other rings or fields: integers, for instance, or number fields. For number
Hasse_principle
Computer network that connects devices over a limited area
A local area network (LAN) is a computer network that interconnects computers within a limited area such as a residence, campus, or building, and has
Local_area_network
Region of the frontal cortex of the brain
2010). "Performance monitoring local field potentials in the medial frontal cortex of primates: supplementary eye field". Journal of Neurophysiology. 104
Supplementary_eye_field
Algebraic variety with a group structure
algebraic groups. If the field k {\displaystyle k} is a local field (for instance the real or complex numbers, or a p-adic field) and G {\displaystyle \mathrm
Algebraic_group
American physicist
implementations. Boyd has performed fundamental studies of the nature of local field effects in optical materials including dense atomic vapors. A key result
Robert_W._Boyd
Disappearance of a species from a specific area
Local extinction refers to the complete disappearance of a species (or other taxon) from a specified geographic area, region, or habitat while that species
Local_extinction
Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity
Explicit_reciprocity_law
is endowed with the inductive limit topology.) On a non-archimedean local field K {\displaystyle K} , a Schwartz–Bruhat function is a locally constant
Schwartz–Bruhat_function
algebras over a field. The concept is named after Helmut Hasse. The invariant plays a role in local class field theory. Let K be a local field with valuation
Hasse_invariant_of_an_algebra
Team sport played with sticks and a ball
Hockey, or field hockey in North America, is a fast-paced team sport in which two teams of eleven players (ten field players and one goalkeeper) use curved
Field_hockey
Field composed from other elementary fields
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
Composite_field
irreducible complex smooth representations of a general linear group over a local field in terms of cuspidal representations. Bernstein, J. (1992), Representations
Bernstein–Zelevinsky classification
Bernstein–Zelevinsky_classification
Topics referred to by the same term
mathematics, local duality may refer to: Local Tate duality of modules over a Galois group of a local field Grothendieck local duality of modules over local rings
Local_duality
Mathematical terminology
modules for extensions of local or global fields and their group cohomology is an important tool in number theory. Given a field K, the multiplicative group
Galois_representation
Mathematical group representations with same data
classes of) irreducible representations of a reductive group over a local field, that are L-indistinguishable, meaning they have the same Langlands parameter
L-packet
(Mathematical) ring with a unique maximal ideal
algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies commutative local rings and
Local_ring
Algebraic structure
In algebra, a field K {\displaystyle K} is perfect if any one of the following equivalent conditions holds: Every irreducible polynomial over K {\displaystyle
Perfect_field
Special group in linear algebra
subgroup is a subgroup of a reductive algebraic group over a nonarchimedean local field that is analogous to a Borel subgroup of an algebraic group. A parahoric
Iwahori_subgroup
Local ring in which Hensel's lemma holds
over a field are Henselian. A local ring that is integral over a Henselian ring is Henselian. The Henselization of a local ring is a Henselian local ring
Henselian_ring
Galois extension whose Galois group is abelian
number fields, function fields of algebraic curves over finite fields, and local fields. There are two slightly different definitions of the term cyclotomic
Abelian_extension
1989 film by Phil Alden Robinson
was then blacked out and local extras drove their vehicles to the field from Commercial Club Park. Riedel worked with local radio stations 92.9 KAT FM
Field_of_Dreams
Topics referred to by the same term
local symbol used to formulate Weil reciprocity A Steinberg symbol on a local field This disambiguation page lists mathematics articles associated with the
Local_symbol
measurements, which forms a local vector field. They can then determine a global vector field consistent with this local field. This is usually done by a
Vector_field_reconstruction
Function in algebra
theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra
Valuation_(algebra)
Topics referred to by the same term
fields from physics to the social sciences. Scalar potential, a scalar field whose gradient is a given vector field Vector potential, a vector field whose
Potential_(disambiguation)
Medications to reversibly block pain
A local anesthetic (LA) is a medication that causes absence of all sensation (including pain) in a specific body part without loss of consciousness, providing
Local_anesthetic
head-to-head result; 6) field goals for. All times are local (UTC+9) First match(es) will be played: 18 September 2026. Source: FIH Field hockey at the 2026
Field hockey at the 2026 Asian Games – Men's tournament
Field_hockey_at_the_2026_Asian_Games_–_Men's_tournament
Mathematical group
field extension is a symmetry group characterizing how it extends the base field. Each element of the Galois group is a transformation of the field extension
Galois_group
minority stayed with Field in a reduced organization. According to one report, from a hostile source, when two members of the New York local F. L Demby and
Fieldites
Branching out of a mathematical structure
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
Ramification_(mathematics)
Type of ring in commutative algebra
Frobenius morphism. Every field is a regular local ring. These have (Krull) dimension 0. In fact, the fields are exactly the regular local rings of dimension
Regular_local_ring
Mathematical theorem
isomorphisms themselves, this is the content of local reciprocity law, key result in local class field theory. A cohomological proof of the global reciprocity
Artin_reciprocity
conductor of an elliptic curve over the field of rational numbers (or more generally a local or global field) is an integral ideal, which is analogous
Conductor of an elliptic curve
Conductor_of_an_elliptic_curve
American theoretical physicist (1918–1994)
radar work, and he used these methods to formulate quantum field theory in terms of local Green's functions in a relativistically invariant way. This
Julian_Schwinger
Special fields Over a finite field, d = 1; over the reals, d = 1 or 2; over a p-adic field or a number field, or any local or global function field, d is
List of irreducible Tits indices
List_of_irreducible_Tits_indices
Concept in number theory
combines all local versions of a global field into one object. For the rational numbers, these local versions include the real numbers and the fields of p {\displaystyle
Adele_ring
Concept in abstract algebra
equivalent conditions: R {\displaystyle R} is a local ring, a principal ideal domain, and not a field. R {\displaystyle R} is a valuation ring with a
Discrete_valuation_ring
Neural mechanism
neurons occurs progressively earlier in relation to the phase of the local field potential oscillation with each successive cycle. In place cells, a type
Phase_precession
Noetherian local ring is a ring of formal power series over a field. (Equicharacteristic means that the local ring and its residue field have the same
Cohen_structure_theorem
reflects the local magnetic field produced at the sodium nucleus by the magnetization of the conduction electrons. The average local field in sodium augments
Knight_shift
Suburb of Sydney, New South Wales, Australia
business district, in the local government area of Camden Council. The area now known as Catherine Field (or Catherine Fields) was originally home to the
Catherine_Field
Concept in class field theory
modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F {\displaystyle F} , its Weil group is generally
Weil_group
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD
LOCAL FIELD