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Four mathematical theorems
K_{i}(C)} . The localization theorem generalizes the localization theorem for abelian categories. Waldhausen Localization Theorem—Let A {\displaystyle
Basic theorems in algebraic K-theory
Basic_theorems_in_algebraic_K-theory
In mathematics, particularly in integral calculus, the localization theorem allows, under certain conditions, to infer the nullity of a function given
Localization_theorem
Topics referred to by the same term
Look up localization, L10n, or localize in Wiktionary, the free dictionary. Localization or localisation may refer to: Localization of function, locating
Localization
Geometry formula
formula, which in turns gives Kirillov's character formula. The localization theorem for equivariant cohomology in non-rational coefficients is discussed
Localization formula for equivariant cohomology
Localization_formula_for_equivariant_cohomology
Algebraic topology theory
. The localization theorem is one of the most powerful tools in equivariant cohomology. Equivariant differential form Kirwan map Localization formula
Equivariant_cohomology
has been developed by Bloch and Marc Levine. In more precise terms, a theorem of Voevodsky implies: for a smooth scheme X over a field and integers p
Bloch's_higher_Chow_group
Theorem in relativistic quantum mechanics
initial localization region can be weakened to a suitably exponential decay of the localization probability at the initial time. The localization threshold
Hegerfeldt's_theorem
Mathematical concept
{\displaystyle {\mathbb {Q}}} . Here, the Serre quotient behaves like a localization. The Serre quotient A / B {\displaystyle {\mathcal {A}}/{\mathcal {B}}}
Quotient of an abelian category
Quotient_of_an_abelian_category
(1984) showed how to deduce the Duistermaat–Heckman formula from a localization theorem for equivariant cohomology. Berline, Nicole; Vergne, Michele (1982)
Duistermaat–Heckman_formula
representation theory and algebraic geometry, the Beilinson–Bernstein localization theorem relates D-modules on flag varieties G/B to representations of the
Beilinson–Bernstein localization
Beilinson–Bernstein_localization
Algebraic structure
non-commutative unitary rings R. The resulting theorem is sometimes known as the Jacobson–Azumaya theorem. Localization is a systematic method of adding multiplicative
Noncommutative_ring
fixed-point theorem holds in the setting of equivariant (algebraic) K-theory. Let X be an equivariant algebraic scheme. Localization theorem—Given a closed
Equivariant algebraic K-theory
Equivariant_algebraic_K-theory
Theorem in axiomatic quantum field theory
distance, creating a unit vector localized outside the region requires operators of ever increasing operator norm. This theorem is also cited in connection
Reeh–Schlieder_theorem
Physics theorem argued by G. H. Derrick
Derrick's theorem is an argument by physicist G. H. Derrick which shows that stationary localized solutions to a nonlinear wave equation or nonlinear
Derrick's_theorem
Branch of mathematics
Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. Bott periodicity KK-theory KR-theory List of cohomology
K-theory
Theorem in political science
In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a one-dimensional political
Median_voter_theorem
a localization of an ∞-category is an ∞-category obtained by inverting some maps. An ∞-category is a presentable ∞-category if it is a localization of
Localization_of_an_∞-category
Construction of a ring of fractions
generally talks of "the localization by the powers of an element" rather than of "the localization by an element". The localization of a ring R by a multiplicative
Localization (commutative algebra)
Localization_(commutative_algebra)
Higher categorical generalization of a topos
and an (accessible) left exact localization functor from the ∞-category of presheaves of spaces on C to X. A theorem of Lurie states that an ∞-category
∞-topos
the localization of the category is unique up to unique isomorphism of categories, provided that it exists. One construction of the localization is done
Localization_of_a_category
Various mathematical dualites
Robert MacPherson. Equivariant cohomology, Koszul duality, and the localization theorem. Inventiones Mathematicae 131 (1998). Joseph Bernstein, Israel Gelfand
Koszul_duality
Theorem in commutative algebra
ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a commutative Noetherian ring. The theorem is
Krull's principal ideal theorem
Krull's_principal_ideal_theorem
Theorem in category theory
theorem, Russell's paradox, Gödel's first incompleteness theorem, Turing's solution to the Entscheidungsproblem, and Tarski's undefinability theorem.
Lawvere's_fixed-point_theorem
Theorem of physical impossibility
Bell's theorem Kochen–Specker theorem PBR theorem No-hiding theorem No-cloning theorem Quantum no-deleting theorem No-teleportation theorem No-broadcast
No-go_theorem
Theorem in quantum mechanics
The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position
Ehrenfest_theorem
On representability of a contravariant functor on the category of connected CW complexes
CW-complexes is equivalent to the localization of the category of all topological spaces at the weak homotopy equivalences, the theorem can equivalently be stated
Brown's representability theorem
Brown's_representability_theorem
Branch of mathematics
{\displaystyle X} itself. The theorem was proved by Hopkins and Ravenel. Let L E ( n ) {\displaystyle L_{E(n)}} denotes the Bousfield localization with respect to the
Chromatic_homotopy_theory
On when an element of the coefficient ring of a ring spectrum is nilpotent
In algebraic topology, the nilpotence theorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of
Nilpotence_theorem
Type of commutative ring in mathematics
who proved the unmixedness theorem for polynomial rings, and for Irvin Cohen (1946), who proved the unmixedness theorem for formal power series rings
Cohen–Macaulay_ring
Theorem of algebraic geometry and commutative algebra
In algebraic geometry, Zariski's main theorem, proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly
Zariski's_main_theorem
Abelian categories, while abstractly defined, are in fact concrete categories of modules
Mitchell's embedding theorem, also known as the Freyd–Mitchell theorem or the full embedding theorem, is a result about small abelian categories; it states
Mitchell's_embedding_theorem
Impossibility of straightforward game forms
In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that
Gibbard's_theorem
Physics theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete
Virial_theorem
Expressing a measure as an integral of another
In mathematics, the Radon–Nikodym theorem, named after Johann Radon and Otto M. Nikodym, is a result in measure theory that expresses the relationship
Radon–Nikodym_theorem
Branch of algebra that studies commutative rings
Lasker–Noether theorem, given here, may be seen as a certain generalization of the fundamental theorem of arithmetic: Lasker-Noether Theorem—Let R be a commutative
Commutative_algebra
French mathematician (1933–2015)
category. This theorem, later vastly generalized by Alexander L. Rosenberg and now known as the Gabriel-Rosenberg reconstruction theorem, forms a starting
Pierre_Gabriel
American mathematician
scheme, and the proof for localization theorems in algebraic K-theory which include the case of non-regular schemes (Theorem 2.1). Thomason also proved
Robert_Wayne_Thomason
In algebra, expression of an ideal as the intersection of ideals of a specific type
In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection
Primary_decomposition
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
the Balian–Low theorem in Fourier analysis is named for Roger Balian and Francis E. Low. The theorem states that there is no well-localized window function
Balian–Low_theorem
British-Lebanese mathematician (1929–2019)
in equivariant cohomology, which was a consequence of well-known localization theorems. Atiyah showed that the moment map was closely related to geometric
Michael_Atiyah
Result in social choice theory
The McKelvey–Schofield chaos theorem is a result in social choice theory. It states that if preferences are defined over a multidimensional policy space
McKelvey–Schofield chaos theorem
McKelvey–Schofield_chaos_theorem
Robert (1998). "Equivariant cohomology, Koszul duality, and the localization theorem" (PDF). Inventiones Mathematicae. 131: 25–83. CiteSeerX 10.1.1.42
GKM_variety
Commutative algebra studies commutative rings, their ideals, and modules over such rings
Completion (ring theory) Formal power series Localization of a ring Local ring Regular local ring Localization of a module Valuation (mathematics) Discrete
List of commutative algebra topics
List_of_commutative_algebra_topics
Branch of mathematics that studies algebraic structures
basis theorem Hopkins–Levitzki theorem Krull's principal ideal theorem Levitzky's theorem Galois theory Abel–Ruffini theorem Wedderburn–Artin theorem Jacobson
List of abstract algebra topics
List_of_abstract_algebra_topics
Mathematical theorem regarding decomposability of measure spaces
counting measure on some discrete space. The theorem is due to Dorothy Maharam. It was extended to localizable measure spaces by Irving Segal. The result
Maharam's_theorem
Algebraic structure
For any (not necessarily local) ring R, the localization Rp at a prime ideal p is local. This localization reflects the geometric properties of Spec R
Commutative_ring
I. Pokhozhaev and is similar to the virial theorem. This relation is also known as G.H. Derrick's theorem. Similar identities can be derived for other
Pokhozhaev's_identity
No-go theorem pertaining the triviality of space-time and internal symmetries
In theoretical physics, the Coleman–Mandula theorem is a no-go theorem stating that spacetime and internal symmetries can only combine in a trivial way
Coleman–Mandula_theorem
Theory and paradigm of statistics
Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability
Bayesian_statistics
Algebraic structure
under localization; 2 → 3 is trivial; 3 → 1 results from the preservation of integral closure under localization, the exactness of localization, and the
Integrally_closed_domain
American theoretical physicist (1923–2020)
called Anderson localization (the idea that extended states can be localized by the presence of disorder in a system) and Anderson's theorem (concerning impurity
Philip_W._Anderson
Theorem in theoretical computer science
database theory, the PACELC design principle is an extension to the CAP theorem. It states that in case of network partitioning (P) in a distributed computer
PACELC_design_principle
usefulness of the theorem stems from the fact, that in order to form the bound, one only needs the minimum number of generators of all localizations M p {\displaystyle
Forster–Swan_theorem
Algebraic formula
theorem implies that a Noetherian local ring is regular if, and only if, it has finite global dimension. In turn this implies that the localization of
Auslander–Buchsbaum_formula
Type of ring in commutative algebra
Noetherian ring, such that the localization at every prime ideal is a regular local ring: that is, every such localization has the property that the minimal
Regular_local_ring
Type of integral domain
Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial
Unique_factorization_domain
British statistician (c. 1701 – 1761)
who is known for formulating a specific case of the theorem that bears his name: Bayes' theorem. Bayes never published what would become his most famous
Thomas_Bayes
Explicitly describes the universal enveloping algebra of a Lie algebra
specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping
Poincaré–Birkhoff–Witt theorem
Poincaré–Birkhoff–Witt_theorem
Scheme for obtaining the position operator
In quantum field theory, Newton–Wigner localization is a scheme for obtaining a position operator for massive relativistic quantum particles. It is named
Newton–Wigner_localization
American mathematician
Robert (1998), "Equivariant cohomology, Koszul duality, and the localization theorem", Inventiones Mathematicae, 131: 25–83, CiteSeerX 10.1.1.42.6450
Robert_Kottwitz
Pathological behavior by an apportionment rule
can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution that
Apportionment_paradox
(Mathematical) ring with a unique maximal ideal
_{(2)}} , the integers localized at 2. More generally, given any commutative ring R and any prime ideal P of R, the localization of R at P is local; the
Local_ring
Computational quantum mechanical modelling method to investigate electronic structure
Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence
Density_functional_theory
Mathematical theorem
In mathematics, the Gabriel–Popescu theorem is an embedding theorem for certain abelian categories, introduced by Pierre Gabriel and Nicolae Popescu (1964)
Gabriel–Popescu_theorem
American mathematician (born 1936)
showing that tight closure does not commute with localization. The first proof of Monsky's theorem, published in 1970, which states that a square cannot
Paul_Monsky
Distance function defined between probability distributions
005. ISSN 1292-8119. (See Theorem 2.9.) Peyre R (October 2018). "Comparison between W2 distance and Ḣ−1 norm, and localization of Wasserstein distance"
Wasserstein_metric
Algebraic structure with addition and multiplication
is called the localization of R with respect to S. For example, if R is a commutative ring and f an element in R, then the localization R [ f − 1 ] {\displaystyle
Ring_(mathematics)
Zero divisors in a module
consider localization of the R-module M, M S = M ⊗ R R S , {\displaystyle M_{S}=M\otimes _{R}R_{S},} which is a module over the localization RS. There
Torsion_(algebra)
Process forming a path from many random steps
approximation theorem. The convergence of a random walk toward the Wiener process is controlled by the central limit theorem, and by Donsker's theorem. For a
Random_walk
{\displaystyle T} (or sometimes S T {\displaystyle ST} ) is also called the localization functor, and S {\displaystyle S} the section functor. The section functor
Localizing_subcategory
Social choice theorem on superiority of majority voting
In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function
May's_theorem
Theorem in geometry
various generalizations of the Riemann–Roch theorem; among the most famous is the Grothendieck–Riemann–Roch theorem, which is further generalized by the formulation
Riemann–Roch-type_theorem
American mathematician (born 1941)
particularly motivating mathematical theorem. The change was prompted by a special case of the uniformization theorem, according to which, in his own words:
Dennis_Sullivan
Technique used for elections
Localized or local list systems of party-list proportional representation hold elections in small (local) electoral districts, while still maintaining
Localized_list
Mathematical transform that expresses a function of time as a function of frequency
sufficient regularity and decay properties is given by the Fourier inversion theorem, i.e., Inverse transform The functions f {\displaystyle f} and f ^ {\displaystyle
Fourier_transform
Theorem in theoretical physics
In theoretical physics, the Haag–Łopuszański–Sohnius theorem states that if both commutating and anticommutating generators are considered, then the only
Haag–Łopuszański–Sohnius theorem
Haag–Łopuszański–Sohnius_theorem
Direct summand of a free module (mathematics)
locally free (in the sense that its localization at every prime ideal is free over the corresponding localization of the ring). The converse is true for
Projective_module
Mathematical theories
picture. These are forms of the localization approach. In group theory, local analysis was started by the Sylow theorems, which contain significant information
Local_analysis
Type of artificial neural network architecture
architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs),
Kolmogorov–Arnold_Networks
Subject area in mathematics
the "localization sequence") relating the K-theory of a variety X and an open subset U. Quillen was unable to prove the existence of the localization sequence
Algebraic_K-theory
Voting systems that use ranked ballots
These models give rise to an influential theorem—the median voter theorem—attributed to Duncan Black. This theorem stipulates that within a broad range of
Ranked_voting
Tendency of bodies towards thermal equilibrium
The process of equilibration can be described using the H-theorem or the relaxation theorem, see also entropy production. Broadly-speaking, classical
Thermalisation
In mathematics, Joyal's theorem is a theorem in homotopy theory that provides necessary and sufficient conditions for the solvability of a certain lifting
Joyal's extension and lifting theorems
Joyal's_extension_and_lifting_theorems
Theorem in algebraic topology about the complex K-theory spectrum
of mathematics, Snaith's theorem, introduced by Victor Snaith, identifies the complex K-theory spectrum with the localization of the suspension spectrum
Snaith's_theorem
\phi :A\to A_{\mathfrak {p}}} is the localization map, since the integral equation persists after localization. If g A = ∩ i q i {\displaystyle gA=\cap
Serre's criterion for normality
Serre's_criterion_for_normality
social choice functions, and is a condition for Arrow's impossibility theorem. With unrestricted domain, the social welfare function accounts for all
Unrestricted_domain
American theoretical physicist
mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of
Edward_Witten
Mathematical ring with well-behaved ideals
reasoning). Every localization of a commutative Noetherian ring is Noetherian. A consequence of the Akizuki–Hopkins–Levitzki theorem is that every left
Noetherian_ring
Theorem in classical electromagnetism
classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources)
Reciprocity (electromagnetism)
Reciprocity_(electromagnetism)
measurable is a decomposable measure that is not σ-finite. Fubini's theorem and Tonelli's theorem hold for σ-finite measures but can fail for this measure. Counting
Decomposable_measure
Ring in which every ideal is principal
Chinese Remainder theorem to a minimal primary decomposition of the zero ideal. There is also the following result, due to Hungerford: Theorem (Hungerford):
Principal_ideal_ring
Projective variety that is also an algebraic group
special case, which is important also from the viewpoint of number theory. Localization techniques lead naturally from abelian varieties defined over number
Abelian_variety
Phenomenon in thermal physics
doing so. Localization enables symmetry breaking orders at finite energy densities, forbidden in equilibrium by the Peierls-Mermin-Wagner Theorems. Let us
Localization-protected quantum order
Localization-protected_quantum_order
Newton–Wigner localization Polynomial Wigner–Ville distribution Thomas–Wigner rotation Wigner interpretation Von Neumann–Wigner theorem Wigner 3-j symbols
List of things named after Eugene Wigner
List_of_things_named_after_Eugene_Wigner
Algebra with unique prime factorization
requirement that a Dedekind domain not be a field. Many more authors state theorems for Dedekind domains with the implicit proviso that they may require trivial
Dedekind_domain
Fourteenth letter in the Greek alphabet
Taylor's theorem that falls between the limits a and b A number used in error approximations for formulas that are applications of Taylor's theorem, such
Xi_(letter)
Ring in abstract algebra
ring is complete. A quotient and localization of an Artinian ring is Artinian. One version of the Wedderburn–Artin theorem states that a simple Artinian
Artinian_ring
Electoral systems with independent candidate ratings
impossibility theorem, a theorem on the limitations of ranked-choice voting Gibbard's theorem, a generalization of the Gibbard-Satterthwaite theorem applicable
Rated_voting
Swiss mathematician, academic and researcher
properties of homotopy groups of K-theory localization. 1968 - Silver Medal, ETH Zurich[citation needed] Localization of Nilpotent Groups and Spaces (1975)
Guido_Mislin
LOCALIZATION THEOREM
LOCALIZATION THEOREM
LOCALIZATION THEOREM
LOCALIZATION THEOREM
Biblical
admiration; perfection; consummation
Boy/Male
Teutonic American English French Hebrew
Noble fighter.
Boy/Male
Muslim
Worshippers
Surname or Lastname
English and Scottish
English and Scottish : occupational name for a clerk or scribe, from Latin scriptor ‘writer’, ‘clerk’. The name has been altered from its original Latin form through association with the more familiar English word scripture ‘Bible’.
Boy/Male
American, Australian, British, Christian, English, Welsh
Prized; Form of David; Beloved; Dear One
Surname or Lastname
English
English : habitational name from any of the various minor places, for example Start Point in Devon, named from Old English steort ‘tail’, in the transferred sense of a promontory or spur of a hill.
Boy/Male
British, English
Counsel Power
Girl/Female
Muslim
Boy/Male
Hebrew American German Shakespearean
Jehovah is God.
Girl/Female
Latin
Young. In Roman mythology Juno was protectress of women and of marriage. In modern times June is...
LOCALIZATION THEOREM
LOCALIZATION THEOREM
LOCALIZATION THEOREM
LOCALIZATION THEOREM
LOCALIZATION THEOREM
n.
One who constructs theorems.
n.
Explanation in a moral sense.
n.
Domination of the head in animal life as expressed in the physical structure; localization of important organs or parts in or near the head, in animal development.
n.
The act of making legal.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
n.
The act of vocalizing, or the state of being vocalized.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
n.
The act of moralizing; moral reflections or discourse.
n.
The act of focalizing or bringing to a focus, or the state of being focalized.
a.
Theorematic.
n.
The exercise of the vocal organs; vocalization.
n.
Act of localizing, or state of being localized.
n.
That which is considered and established as a principle; hence, sometimes, a rule.
n.
A numerical coefficient in any particular case of the binomial theorem.
n.
A statement of a principle to be demonstrated.
n.
The doctrine of the localization of disease, or which refers it always to a material lesion of an organ.
n.
The formation and utterance of vocal sounds.
v. t.
To formulate into a theorem.
a.
Alt. of Theorematical
n.
The act of making loyal to a king.