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Néron model

In algebraic geometry, the Néron model (or Néron minimal model, or minimal model) for an abelian variety AK defined over the field of fractions K of a Dedekind domain R is the "push-forward" of AK from Spec(K) to Spec(R), in other words the "best possible" group scheme AR defined over R corresponding to AK.

Products, Definition & The Néron model of an elliptic curve

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Definition

SmoothSeparatedSmoothUniversalGrothendieck topology
8 related topics

The Néron model of an elliptic curve

Elliptic curveTate's algorithmSpecial fiber
3 related topics

Properties

ÉtaleAbelian scheme
2 related topics

Overview

Algebraic geometryAbelian varietyField of fractionsDedekind domainGroup scheme
8 related topics

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Definition

Properties

The Néron model of an elliptic curve

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Néron model

Nodes26
Edges25
Triples67
Avg. degree1.92
Density0.076923
Components1

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Néron model

Top relations

related to References · 45
Néron model → A345, A347, Académie, André, Arithmetic, Artin, Berlin, BF02684271, Comptes Rendus, Conn, Cornell, Dolgachev, EMS PressNéron, Encyclopedia, Ergebnisse, Grenzgebiete, IHÉS, ISBN, Joseph, Lock-gray-alt-2
related to Definition · 8
Néron model → AK, AR, Dedekind, If, In, Néron, Suppose, Then
related to The Néron model of an elliptic curve · 8
Néron model → AK, First, Its, Néron, Tate's, The, The Néron, This
related to Properties · 4
Néron model → An Abelian, AR, Néron, The

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Important terminology

néron model scheme abelian models smooth ak group minimal field dedekind domain algebraic variety spec ar varieties raynaud mr elliptic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
toriinstance ofNéron models exist as well for certain commutative groups other than abelian varieties0.80text
but these are only locally of finite typeinstance ofNéron models exist as well for certain commutative groups other than abelian varieties0.80text
Néron modelrelated to DefinitionSuppose0.60section
Néron modelrelated to DefinitionDedekind0.60section
Néron modelrelated to DefinitionAK0.60section
Néron modelrelated to DefinitionThen0.60section
Néron modelrelated to DefinitionNéron0.60section
Néron modelrelated to DefinitionAR0.60section
Néron modelrelated to DefinitionIn0.60section
Néron modelrelated to DefinitionIf0.60section
Néron modelrelated to PropertiesThe0.60section
Néron modelrelated to PropertiesNéron0.60section

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