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Stack (mathematics)

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist.

History, Motivation and history & Other types of stack

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Examples

Quasi-coherent sheaves on algebraic stacks

Other types of stack

Set-theoretical problems

Pedagogical

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Map overview Semantic statistics

Stack (mathematics)

Nodes105
Edges104
Triples2
Avg. degree1.98
Density0.019048
Components1

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Important terminology

stack displaystyle stacks algebraic moduli spaces one morphism category topology curves group grothendieck mumford space scheme descent quotient sets schemes

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
an infinite projective spaceinstance ofOther moduli stacksA Picard stack generalizes a Picard variety.The moduli stack of formal group laws classifies formal group laws.An ind-scheme0.80text
a formal scheme is a stack.A moduli stack of shtukas is used in geometric Langlands programinstance ofOther moduli stacksA Picard stack generalizes a Picard variety.The moduli stack of formal group laws classifies formal group laws.An ind-scheme0.80text

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