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Algebraic stack

In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves M g , n…

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Overview

Definition

Structure sheaf

Examples

Papers

Applications

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Map overview Semantic statistics

Algebraic stack

Nodes61
Edges60
Triples69
Avg. degree1.97
Density0.032787
Components1

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Algebraic stack

Top relations

related to Papers · 23
Algebraic stack → Adic Categories, Advances, Algebraic Stacks, Alper, American Mathematical Society, Archived, Behrend, CS1, David, Derived, Guide, Hall, ISBN, Jack, Jarod, Kai, Literature, Mathematics, Memoirs, PDF
related to Deligne–Mumford stacks · 16
Algebraic stack → Algebraic, Also, Artin, Deligne, Deligne-Mumford, Etale, For, If, In, Lie, Mumford, Note, Only, The, The Etale, This
related to Artin's Axioms · 6
Algebraic stack → Algebraic, Artin Algebraization, Axioms, Jarod Alper, Look, Quotient Stacks
is a · 4
Algebraic stack → algebraic space, fibered category p, object pulled back from a universal structure sheaf O, vast generalization of algebraic spaces
related to Defining algebraic stacks over other topologies · 4
Algebraic stack → F/S, Grothendieck, It, Using
related to Algebraic stacks · 3
Algebraic stack → It, Sch, Then
related to Classifying stacks · 3
Algebraic stack → BG, In, Many
related to Other · 3
Algebraic stack → Examples, Grothendieck, StacksNotes
related to Structure sheaf · 3
Algebraic stack → Sch/S, The, This
related to Motivation · 2
Algebraic stack → For, One

Important terminology Word statistics

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Important terminology

displaystyle algebraic mathcal stacks stack fppf sch moduli scheme fibered representable space spaces category groupoids theory grothendieck smooth sheaf associated

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Algebraic stackis avast generalization of algebraic spaces0.90text
Algebraic stackis afibered category p0.90text
Algebraic stackis aalgebraic space0.90text
Algebraic stackis aobject pulled back from a universal structure sheaf O0.90text
Algebraic stackrelated to Algebraic stacksIt0.60section
Algebraic stackrelated to Algebraic stacksSch0.60section
Algebraic stackrelated to Algebraic stacksThen0.60section
Algebraic stackrelated to Artin's AxiomsLook0.60section
Algebraic stackrelated to Artin's AxiomsAxioms0.60section
Algebraic stackrelated to Artin's AxiomsAlgebraic0.60section
Algebraic stackrelated to Artin's AxiomsArtin Algebraization0.60section
Algebraic stackrelated to Artin's AxiomsQuotient Stacks0.60section

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