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Group scheme

In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This…

Definition, Constructions & Basic properties

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Overview

Definition

Constructions

Examples

Basic properties

Finite flat group schemes

Cartier duality

Dieudonné modules

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Map overview Semantic statistics

Group scheme

Nodes92
Edges91
Triples144
Avg. degree1.98
Density0.021739
Components1

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Group scheme

Top relations

related to References · 53
Group scheme → Alexandre Grothendieck, Amsterdam, Arithmetic, Berlin, Berthelot, Bois Marie, Breen, Co, Conn, Cornell, Demazure, Dieudonné Crystalline IILaumon, Fermat's Last TheoremWaterhouse, Finite, Fourier, French, Gabriel, Gary, Graduate Texts, Group
related to Dieudonné modules · 22
Group scheme → Cartier, CW, D-modules, Dieudonne, Dieudonné, Finite, Frobenius, FV, Galois, Grothendieck, Many, Oda's, Rham, Shimura, Taniyama, The, The Dieudonné, This, Verschiebung, Wiles's
related to Constructions · 19
Group scheme → As, Base, Finite, For, G-action, Galois, Given, Group, GS, However, If, Kernels, More, OT, Representability, S-scheme, The, Weil, When
related to Examples · 16
Group scheme → A1, Algebraic, Alternatively, As, For, Ga, GLn, Gm, If, In, It, Over, S-scheme, Spec, The, Unlike
related to Basic properties · 11
Group scheme → Affine, Any, For, G0, Gred, Hopf, Let G0, OS-algebra, Suppose, The, Then
related to Finite flat group schemes · 9
Group scheme → Among, For, More, OG, OS-module, Over, Raynaud's, The, There
related to Definition · 4
Group scheme → S-scheme, See, That, Yoneda
is a · 3
Group scheme → group object in a category of schemes that has fiber products and some final object S, spectrum of a commutative Hopf algebra, type of object from algebraic geometry equipped with a composition law
related to Cartier duality · 2
Group scheme → Cartier, Pontryagin
see also · 1
Group scheme → Fundamental

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Important terminology

group scheme schemes finite affine one groups flat base functor commutative structure algebraic spectrum connected abelian field theory action s-scheme

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Group schemeis atype of object from algebraic geometry equipped with a composition law0.90text
Group schemeis agroup object in a category of schemes that has fiber products and some final object S0.90text
Group schemeis aspectrum of a commutative Hopf algebra0.90text
Spec Ainstance ofOver an affine base0.80text
it is the spectrum of the ring Ainstance ofOver an affine base0.80text
it is the spectrum of Ainstance ofOver an affine base0.80text
it is the spectrum of the polynomial ring Ainstance ofOver an affine base0.80text
Group schemerelated to Basic propertiesSuppose0.60section
Group schemerelated to Basic propertiesLet G00.60section
Group schemerelated to Basic propertiesThen0.60section
Group schemerelated to Basic propertiesG00.60section
Group schemerelated to Basic propertiesGred0.60section

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    Min side: 3
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