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Derived scheme

In algebraic geometry, a derived scheme is a homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions such as differential graded algebras, commutative simplicial rings, or commutative ring spectra.

Differential graded scheme, Overview & Cotangent complex

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Overview

Differential graded scheme

Cotangent complex

Tangent complexes

Derived critical locus

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Derived scheme

Nodes40
Edges39
Triples16
Avg. degree1.95
Density0.05
Components1

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Derived scheme

Top relations

related to Derived schemes in complex Morse theory · 5
Derived scheme → Derived, For, If, Omega, Then
related to Connection with differential graded rings and examples · 4
Derived scheme → For, Just, Koszul, One
related to Polynomial functions · 2
Derived scheme → Given, Then
is a · 1
Derived scheme → homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions such as differential graded algebras

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Important terminology

derived displaystyle scheme complex graded differential geometry mathbb bullet affine rings ring cotangent algebraic commutative stack characteristic algebra koszul simplicial

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Derived schemeis ahomotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions such as differential graded algebras0.90text
differential graded algebrasinstance ofa derived scheme is a homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions0.80text
commutative simplicial ringsinstance ofa derived scheme is a homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions0.80text
or commutative ring spectra.From the functor of points point-of-viewinstance ofa derived scheme is a homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions0.80text
a derived scheme is a sheaf X on the category of simplicial commutative rings which admits an open affine coveringinstance ofa derived scheme is a homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived versions0.80text
Derived schemerelated to Connection with differential graded rings and examplesJust0.60section
Derived schemerelated to Connection with differential graded rings and examplesOne0.60section
Derived schemerelated to Connection with differential graded rings and examplesKoszul0.60section
Derived schemerelated to Connection with differential graded rings and examplesFor0.60section
Derived schemerelated to Derived schemes in complex Morse theoryDerived0.60section
Derived schemerelated to Derived schemes in complex Morse theoryFor0.60section
Derived schemerelated to Derived schemes in complex Morse theoryIf0.60section

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