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Mathematical concept
kinds of global fields: Algebraic number field: A finite extension of Q {\displaystyle \mathbb {Q} } Global function field: The function field of an irreducible
Global_field
Algebraic structure with addition, multiplication, and division
are completions of global fields. Ostrowski's theorem asserts that the only completions of Q, a global field, are the local fields Qp and R. Studying
Field_(mathematics)
Branch of algebraic number theory concerned with abelian extensions
local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However,
Class_field_theory
Concept in number theory
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
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts
Earth's_magnetic_field
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
number field or a global function field). It is used to encode ramification data for abelian extensions of a global field. Let K be a global field with
Modulus (algebraic number theory)
Modulus_(algebraic_number_theory)
Third season of the Global Super League
The 2026 Global Super League was the third edition of the Global Super League. The tournament featured five teams from different countries that took part
2026_Global_Super_League
Spread of world views, products, ideas, capital and labor
the field, described globalization as "the compression of the world and the intensification of the consciousness of the world as a whole." In Global Transformations
Globalization
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
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)
Idea that all people have rights and responsibilities from being a member of the world
as the World Service Authority, have advocated global transnational citizenship. The field of global citizenship, as a form of transnationality is transnationalism
Global_citizenship
in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety X over a global field, which measures
Manin_obstruction
Mathematical theorem
is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long line of more concrete
Artin_reciprocity
Field theory is the branch of algebra that studies fields
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 some global field
Glossary_of_field_theory
Semitopological group in abstract algebra
the adelic points of an algebraic group G {\displaystyle G} over a global field K {\displaystyle K} form a topological group denoted G ( A K ) {\displaystyle
Adelic_algebraic_group
generalizes the theory of line bundles on models of finite extensions of global fields. Frobenioids were introduced by Shinichi Mochizuki (2008). The word
Frobenioid
Human-caused changes to climate on Earth
Present-day climate change includes both global warming—the ongoing increase in global average temperature—and its wider effects on Earth's climate system
Climate_change
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
In mathematics, specifically class field theory, a ray class field is an abelian extension of a global field associated with a ray class group of ideal
Ray_class_field
Political and economic patterns of the world
Global politics, also known as world politics, names both the discipline that studies the political and economic patterns of the world and the field that
Global_politics
Japanese printing press manufacturer
With a close inner circle of developers active in installations and global field service, Komori has used over the years Windows-based systems for press
Komori
trace formula from the group SL2 to arbitrary reductive groups over global fields, developed by James Arthur in a long series of papers from 1974 to 2003
Arthur–Selberg_trace_formula
Russian mathematician
and objects from higher class field theory. Fesenko generalized the Iwasawa-Tate theory from 1-dimensional global fields to 2-dimensional arithmetic surfaces
Ivan_Fesenko
Local–global principle for quadratic forms
Helmut Hasse. The same statement holds even more generally for all global fields. The importance of the Hasse–Minkowski theorem lies in the novel paradigm
Hasse–Minkowski_theorem
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
abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field. For an abelian variety A {\displaystyle
Semistable_abelian_variety
Solving integer equations from all modular solutions
joined to form a global solution? One can ask this for other rings or fields: integers, for instance, or number fields. For number fields, rather than reals
Hasse_principle
1994 originators of commercial spam; married American lawyers
first Usenet spammers, but some consider them pioneers in the modern global field of ad spamming. In early 1994, Canter and Siegel contracted with Leigh
Laurence Canter and Martha Siegel
Laurence_Canter_and_Martha_Siegel
American satellite-based radio navigation service
The Global Positioning System (GPS) is a satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta
Global_Positioning_System
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
Mathematical terminology
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
Inaugural season of the Global Super League
The 2024 Global Super League was the inaugural edition of the Global Super League. The tournament featured five teams from different countries that played
2024_Global_Super_League
Reversal of direction of Earth's magnetic field
chemical, physical or biological change. Because Earth's magnetic field is a global phenomenon, similar patterns of magnetic variations at different sites
Geomagnetic_reversal
Abelian group related to division algebras
Q/Z, the Hasse invariant. The case of a global field K (such as a number field) is addressed by global class field theory. If D is a central simple algebra
Brauer_group
Second season of the Global Super League
The 2025 Global Super League was the second edition of the Global Super League. The tournament featured five teams from different countries which played
2025_Global_Super_League
Theorem in algebraic number theory
or global fields to an extension of Galois groups. It was introduced by Shafarevich (1946) for local fields and by Weil (1951) for global fields. Suppose
Shafarevich–Weil_theorem
groups over global fields. The results for number fields are due to Kneser (1966) and Platonov (1969); the function field case, over finite fields, is due
Approximation in algebraic groups
Approximation_in_algebraic_groups
Book about number theory
approach handles all 'A-fields' or global fields, meaning finite algebraic extensions of the field of rational numbers and of the field of rational functions
Basic_Number_Theory
abelian variety A over a number field K; or more generally (for global fields or more general finitely-generated rings or fields). There is some tension here
Arithmetic of abelian varieties
Arithmetic_of_abelian_varieties
surveys 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)
K-groups_of_a_field
Locally compact topological field
of global fields. Moreover, tools like integration and Fourier analysis are available for functions defined on local fields. Given a local field, an
Local_field
Conjectures connecting number theory and geometry
groups over global fields (with subcases corresponding to number fields or function fields). Analogues for finite fields. More general fields, such as function
Langlands_program
American scientist
publications, Field's research emphasizes impacts of climate change, from the molecular to the global scale. His work includes major field experiments on
Christopher_Field
Large cabin business jet
The Bombardier Global Express is a large cabin, long-range business jet designed and manufactured by Bombardier Aviation. Announced in October 1991, it
Bombardier_Global_Express
representations over a local field, while the global theta correspondence relates irreducible automorphic representations over a global field. The theta correspondence
Theta_correspondence
Given a finite group scheme M {\displaystyle M} over a global field k {\displaystyle k} , global Tate duality relates the cohomology of M {\displaystyle
Tate_duality
Industry taxonomy
The Global Industry Classification Standard (GICS) is an industry taxonomy developed in 1999 by MSCI and Standard & Poor's (S&P) for use by the global financial
Global Industry Classification Standard
Global_Industry_Classification_Standard
United Nations Peacekeeping office based in Brindisi, Italy, and Valencia, Spain
which created the Global Field Support Strategy (GFSS) which merged the UNLB and UNSBV into one organization called the "Global Service Centre." The
United Nations Global Service Centre
United_Nations_Global_Service_Centre
over a global field. It is named after André Néron and John Tate. Néron defined the Néron–Tate height as a sum of local heights. Although the global Néron–Tate
Néron–Tate_height
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
Cantonese endonym used in Guangdong and Guangxi
Policy Weitou dialect "香港歷史博物館- Hong Kong Museum of History – Global Field Trip". Global Field Trip. 5 May 2015. Retrieved 17 August 2017. Constable 2005
Punti
divisor) on a global field is an extension of the concept of divisor or fractional ideal. It is a formal linear combination of places of the field with finite
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Algebraic structure
is finitely generated over its prime field (e.g. a finite field, an algebraic number field, a global function field), of characteristic different from p
Tate_module
Field of mathematical analysis
overlaps with global analysis. Global analysis finds application in physics in the study of dynamical systems and topological quantum field theory. Annals
Global_analysis
Global electromagnetic resonances, generated and excited by lightning discharges
extremely low frequency portion of the Earth's electromagnetic field spectrum. They are global electromagnetic resonances generated and excited by lightning
Schumann_resonances
Mathematical concept
{\displaystyle \tau (G)} of a semisimple algebraic group defined over a global field k is the measure of G ( A ) / G ( k ) {\displaystyle G(\mathbb {A} )/G(k)}
Tamagawa_number
describes the abelianization of the Galois group of a local or global field, geometric class field theory describes the abelianized fundamental group of higher
Geometric_class_field_theory
Map raising elements to the pth power, in characteristic p
an abelian extension of global fields, we get a much stronger congruence since it depends only on the prime φ in the base field K. For an example, consider
Frobenius_endomorphism
Group controlling representation theory
automorphic forms are in a sense functorial in the group G, when k is a global field. It is not exactly G with respect to which automorphic forms and representations
Langlands_dual_group
International initiative
The Global Partnership on Artificial Intelligence (GPAI, pronounced "gee-pay") is an international initiative established to guide the responsible development
Global Partnership on Artificial Intelligence
Global_Partnership_on_Artificial_Intelligence
Study of history from a global perspective
World history or global history as a field of historical study examines history from a global perspective. It emerged centuries ago; some leading practitioners
World_history_(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
Mass surveillance across national borders
Global mass surveillance can be defined as the mass surveillance of entire populations across national borders. Its existence was not widely acknowledged
Global_surveillance
Health of populations in a global context
Goals. The field of global health law studies international lawmaking bodies, such as the WHO, and their effect on global health. Global health employs
Global_health
American field service software company
with Technology Crossover Ventures, raising $66 million to transform global field service management. On July 31, 2014, Oracle Corporation announced that
TOA_Technologies
Number system extending the rational numbers
all the above-mentioned completions when E is a number field (or more generally a global field), which are seen as encoding "local" information. This
P-adic_number
Concept in number theory
idele group is a way of packaging the multiplicative arithmetic of a global field at all of its completions at once, so that it contains the information
Idele_group
national field hockey team (recognized as Korea by FIH) represents South Korea in international field hockey competitions. Their best result in the global stage
South Korea men's national field hockey team
South_Korea_men's_national_field_hockey_team
telecommunications technology services it provides." Founded in 2010 as part of the Global Field Support Strategy (GFSS) in UNGA Resolution 64/269, the Regional Service
United Nations Department of Field Support
United_Nations_Department_of_Field_Support
Totally real field Local field p-adic number p-adic analysis Adele ring Idele group Idele class group Adelic algebraic group Global field Hasse principle
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Sri Lankan field hockey player
Dhyan Chand who insisted that Ceylon was the world's sixth best team in global field hockey as he made such a critical statement during Ceylon's 1959/60 tour
Freddie_White_(field_hockey)
Mathematical theory
can be formulated for global fields (as well as local fields), which are classified into number fields or global function fields. Establishing the classical
Geometric Langlands correspondence
Geometric_Langlands_correspondence
Qualifications for participating in the Boston Marathon
presented by Bank of America |". www.baa.org. Retrieved 2024-09-25. "Global Field of Qualifiers Notified of Acceptance into the 128th Boston Marathon presented
Boston Marathon Qualifying Standards
Boston_Marathon_Qualifying_Standards
Private rescue and security company
Global Rescue is a crisis response, medical evacuation and security extraction company with additional services such as field rescue, medical advisory
Global_Rescue
Movement towards political cooperation among transnational actors
the governance of world orders. Other authors conceptualized global governance as a field of practice in which diverse stakeholders, such as public, private
Global_governance
American racecar team
Andretti Global is an American motorsports organization with teams competing in the IndyCar Series, Indy NXT, Formula E, and joint entries in IMSA and
Andretti_Global
Global Engineering Education is a field of study that focuses on the impact of globalization on the engineering industry. Over the past decade or so educators
Global_Engineering_Education
Finitely generated extension field of positive transcendence degree
a finite field). In the context of this analogy, both number fields and function fields over finite fields are usually called "global fields". The study
Algebraic_function_field
separable finite extensions of some function field over a finite field, and G is the Galois group. Global class field theory of characteristic 0: The module
Class_formation
Canadian broadcast TV network
The Global Television Network (more commonly called Global, or occasionally Global TV) is a Canadian English-language terrestrial television network. It
Global_Television_Network
Group-like structure appearing in global fields
structure appearing in global fields. In 1972, D. Shanks first discovered the infrastructure of a real quadratic number field and applied his baby-step
Infrastructure (number theory)
Infrastructure_(number_theory)
SaaS company
Simpro is a global SaaS company that provides cloud-based job and project management software to those in field service and trade contracting industries
Simpro
Measures the relative position of nations' and regions' peacefulness
The Global Peace Index (GPI) is a report produced by the Australia-based NGO Institute for Economics & Peace (IEP) which measures the relative position
Global_Peace_Index
research. As to why, given so vast literature on globalization, military globalization today remains a field of original research is an intriguing question
Military_globalization
International perspective on mental health
all people worldwide." The field focuses on improving the prevention, care, and treatment of mental health disorders globally, along with improving the
Global_mental_health
Academic book by John Baylis, Steve Smith and Patricia Owens
The Globalization of World Politics: An Introduction to International Relations is an introduction to international relations (IR) and offers comprehensive
The Globalization of World Politics
The_Globalization_of_World_Politics
Mercury's small magnetic field
Mercury's magnetic field is approximately a magnetic dipole, apparently global, on the planet of Mercury. Data from Mariner 10 led to its discovery in
Mercury's_magnetic_field
Mathematical object
conjectural group L F {\displaystyle L_{F}} attached to each local or global field F {\displaystyle F} that satisfies properties similar to those of the
Langlands_group
The conjecture holds in the case where F is a local field (such as p-adic field) or a global field with no real embeddings (such as Q(√−1)). This is a
Serre's_conjecture_II
Field of law
Global health law is the field of health law dealing with global health. The field began as an outgrowth of public health law, applying it to the international
Global_health_law
American actress (born 1946)
directors of Vital Voices Global Partnership, an international women's NGO, and has co-hosted the Global Leadership Awards six times. Field is also an advocate
Sally_Field
Non-profit organization
The Solidarity Center is a global nonprofit organization dedicated to supporting workers worldwide. It promotes labor rights, safe workplaces, fair wages
Solidarity_Center
Swedish early warning aircraft
The Saab GlobalEye is a multi-role airborne early warning & control (AEW&C) platform from Swedish defence and security company Saab. In service since April
GlobalEye
Volcanic field in Eritrea
years during the current Holocene epoch. List of volcanic fields "Assab Volcanic Field". Global Volcanism Program. Smithsonian Institution. Retrieved 2021-06-24
Assab_volcanic_field
Related representations, also denoted θ10, occur for Sp4 over local and global fields. Srinivasan (1968) introduced θ10 in her determination of the irreducible
Θ10
American mathematician (1925–2019)
previous approaches to class field theory, which used central division algebras to compute the Brauer group of a global field. Subsequently, Tate introduced
John_Tate_(mathematician)
Boxing management company
Charlie Edwards, Rocky Fielding, Hughie Fury, Michael Conlan, Paddy Barnes, Jamel Herring, and Amansio Paraschiv. MTK Global originally formed as MGM
MTK_Global
Fourth edition of the Global T20 Canada
The 2024 Global T20 Canada was the fourth edition of Global T20 Canada, a Twenty20 professional cricket tournament that was played at the TD Cricket Arena
2024_Global_T20_Canada
Kenyan football club
known as F.C 105 before the Management (Joshua and Ray) teamed up with global field evangelism under Bishop Ben Bahati hence the name G.F.E 105 FC. The club
G.F.E._105
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