Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Algebraic space

In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology.…

Art, Definition & Algebraic spaces and schemes

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Algebraic space. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definition

Algebraic spaces and schemes

Algebraic spaces and analytic spaces

Generalization

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Algebraic space

Nodes45
Edges44
Triples58
Avg. degree1.96
Density0.044444
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Algebraic space

Top relations

related to References · 26
Algebraic space → Abhyankar, Algebraic, Algebraic Spaces, Artin, Berlin, BFb0059750, Bombay Colloquium, Donald, Fundamental Research, ISBN, Lecture Notes, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Mathematics, Michael, MR, New York, Oxford University Press, Shreeram Shankar
related to Algebraic spaces and schemes · 14
Algebraic space → Algebraic, Commutative-group, Every, For, Hironaka's, In, Non-singular, Not, Proper, Quasi-separated, Similar, The, This, Thus
related to Algebraic spaces and analytic spaces · 6
Algebraic space → Algebraic, Hopf, In, It, Moishezon, Roughly
related to External links · 5
Algebraic space → Algebraic, Danilov, EMS PressAlgebraic, Encyclopedia, Mathematics
related to Algebraic spaces as quotients of schemes · 3
Algebraic space → An, Knutson, Some
related to Definition · 2
Algebraic space → There, These
related to Algebraic spaces as sheaves · 1
Algebraic space → An
related to Generalization · 1
Algebraic space → In

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

algebraic spaces schemes space affine quotient étale one scheme analytic defined category proper given group quasi-separated complex mathematics artin finite

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Algebraic spacerelated to Algebraic spaces and analytic spacesAlgebraic0.60section
Algebraic spacerelated to Algebraic spaces and analytic spacesMoishezon0.60section
Algebraic spacerelated to Algebraic spaces and analytic spacesRoughly0.60section
Algebraic spacerelated to Algebraic spaces and analytic spacesIn0.60section
Algebraic spacerelated to Algebraic spaces and analytic spacesHopf0.60section
Algebraic spacerelated to Algebraic spaces and analytic spacesIt0.60section
Algebraic spacerelated to Algebraic spaces and schemesAlgebraic0.60section
Algebraic spacerelated to Algebraic spaces and schemesFor0.60section
Algebraic spacerelated to Algebraic spaces and schemesProper0.60section
Algebraic spacerelated to Algebraic spaces and schemesNon-singular0.60section
Algebraic spacerelated to Algebraic spaces and schemesQuasi-separated0.60section
Algebraic spacerelated to Algebraic spaces and schemesCommutative-group0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.