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Weil restriction

In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic variety X over L, produces another variety ResL/kX, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complicated varieties over smaller fields.

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Examples and applications

Group schemeNumber theoryHodge theoryTannakian categoryHodge structures
17 related topics

Definition

SchemesRepresentableSheavesRight adjointFiber product of schemes
8 related topics

Properties

Algebraic spacesAlgebraic stacks
2 related topics

Weil restrictions vs. Greenberg transforms

Witt vectors
1 related topics

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Overview

Definition

Properties

Examples and applications

Weil restrictions vs. Greenberg transforms

Advanced semantic analysis

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Map overview Semantic statistics

Weil restriction

Nodes40
Edges39
Triples8
Avg. degree1.95
Density0.05
Components1

How this topic connects Entity context

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Weil restriction

Top relations

related to Alternative definition · 5
Weil restriction → For, Let, Res, S'/S, Weil

Important terminology Word statistics

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Important terminology

restriction displaystyle scalars weil fields extension varieties operatorname variety res finite functor group math defined morphism mathbb abelian algebraic schemes

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Artininstance ofpreserving properties0.80text
Deligne-Mumfordinstance ofpreserving properties0.80text
and representabilityinstance ofpreserving properties0.80text
Weil restrictionrelated to Alternative definitionLet0.60section
Weil restrictionrelated to Alternative definitionFor0.60section
Weil restrictionrelated to Alternative definitionRes0.60section
Weil restrictionrelated to Alternative definitionS'/S0.60section
Weil restrictionrelated to Alternative definitionWeil0.60section

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