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Cotangent complex: Works, Properties of the cotangent complex & Early work on cotangent complexes

In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If f : X → Y {\displaystyle f:X\to Y} is a morphism of geometric or algebraic objects, the corresponding cotangent complex L X / Y ∙ {\displaystyle \mathbf {L}…

Language: English [EN]
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Cotangent complex topic overview

The analysis highlights Works, Properties of the cotangent complex and Early work on cotangent complexes as prominent areas in the source structure around Cotangent complex.

Related topics
83
Source areas
7
Connected nodes
90
Extracted relationships
105
Concept neighborhoods
47
Bridge connections
90

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 21 topics
Properties of the cotangent complex · 20 topics
Early work on cotangent complexes · 13 topics
Motivation · 12 topics
Examples · 6 topics
The definition of the cotangent complex · 6 topics
Cotangent complexes in deformation theory · 5 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Suggested research paths

A focused starting point derived from the topic graph, ranked independently of the source article order.

Start with these areas

Less obvious directions

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Motivation

Early work on cotangent complexes

The definition of the cotangent complex

Cotangent complexes in deformation theory

Properties of the cotangent complex

Examples

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.

How Cotangent complex connects Entity context

The extracted context around Cotangent complex shows recurring relationship patterns in the source. For example, Cotangent complex → A-algebra, A-module, André, Annals, As, Avramov, Avramov's, B-modules, B/A, Briggs, Iyengar, Let, Lichtenbaum, Luchezar Avramov, Quillen, Schlessinger, The, This, Thus, Tor Another extracted example is Cotangent complex → Alexander Grothendieck, All, Cartier, Cotangent, Exposé VIII, If, In, It, J/J, Omega, Pierre Berthelot, Riemann-Roch, SGA, The, This, V/Y, X/Y. Use these groups to spot repeated connection types before inspecting the individual relationships.

Cotangent complex

Top relations

related to Characterization of local complete intersections · 20
Cotangent complex → A-algebra, A-module, André, Annals, As, Avramov, Avramov's, B-modules, B/A, Briggs, Iyengar, Let, Lichtenbaum, Luchezar Avramov, Quillen, Schlessinger, The, This, Thus, Tor
related to Early work on cotangent complexes · 17
Cotangent complex → Alexander Grothendieck, All, Cartier, Cotangent, Exposé VIII, If, In, It, J/J, Omega, Pierre Berthelot, Riemann-Roch, SGA, The, This, V/Y, X/Y
related to Closed embeddings in smooth schemes · 11
Cotangent complex → Kähler, Let, Omega, Sch, The, This, To, Using, X/S, X/Y, Y/S
related to Motivation · 11
Cotangent complex → If, In, Kähler, Lichtenbaum, Literally, Most, Omega, Schlessinger, Suppose, The, X/Y
related to Smooth schemes · 10
Cotangent complex → In, In Berthelot's, Kähler, Let, Omega, Sch, Spec, Then, We, X/S
related to The definition of the cotangent complex · 9
Cotangent complex → André, Choose, For, Illusie, Iterating, Quillen, Such, Suppose, The
related to Flat base change · 7
Cotangent complex → A-algebra, A-algebras, If, Suppose, The, Then, Tor
related to Flat descent · 6
Cotangent complex → Amitsur, Bhargav Bhatt, In, More, R-algebras, The
is a · 4
Cotangent complex → common generalisation of the cotangent sheaf, fact that given a morphism of S, same as the Kähler differentials, same as the Kähler differentials.Closed embeddings in smooth schemesLet i
related to Local complete intersection · 3
Cotangent complex → For, More, This

Important terminology

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

Important terminology

displaystyle cotangent complex morphism theory mathbf bullet exact smooth sequence kähler differentials deformation simplicial given algebraic complexes omega morphisms derived

Cotangent complex relationships Subject–Predicate–Object triples

TTTA extracted 105 structured relationships around Cotangent complex. Examples in this analysis include Cotangent complex → is a → common generalisation of the cotangent sheaf and Cotangent complex → is a → fact that given a morphism of S. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Cotangent complexis acommon generalisation of the cotangent sheaf0.90text
Cotangent complexis afact that given a morphism of S0.90text
Cotangent complexis asame as the Kähler differentials.Closed embeddings in smooth schemesLet i0.90text
Cotangent complexis asame as the Kähler differentials0.90text
manifolds or schemesinstance ofnormal bundle and virtual tangent bundle of a map of geometric spaces0.80text
Cotangent complexrelated to Characterization of local complete intersectionsThe0.60section
Cotangent complexrelated to Characterization of local complete intersectionsLet0.60section
Cotangent complexrelated to Characterization of local complete intersectionsA-algebra0.60section
Cotangent complexrelated to Characterization of local complete intersectionsAs0.60section
Cotangent complexrelated to Characterization of local complete intersectionsQuillen0.60section
Cotangent complexrelated to Characterization of local complete intersectionsLichtenbaum0.60section
Cotangent complexrelated to Characterization of local complete intersectionsSchlessinger0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Cotangent complex bring nearby vocabulary together. In this analysis, examples include Cotangent, Displaystyle and Mathbf. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Cotangent complex
    • Cotangent
    • Displaystyle
    • Mathbf
    • Complexes
    • Morphism
    • Bullet
    • Theory
    • Given
    • Omega
    • Differentials
    • Kähler
    • Category
  • cotangent complex
    • Cotangent
    • Displaystyle
    • Morphism
    • Mathbf
    • Complexes
    • Bullet
    • Theory
    • Given
    • Omega
    • Category
    • Differentials
    • Kähler
  • cotangent sheaf
    • Displaystyle
    • Mathbf
    • Complexes
    • Morphism
    • Bullet
    • Theory
    • Given
    • Omega
    • Differentials
    • Kähler
    • Category
    • Object
  • morphism
    • Perfect
    • Smooth
    • Definition
    • Given
    • Differentials
    • Kähler
    • Theory
    • Left
    • One
    • Complexes
    • Sequence
    • Flat
  • deformation theory
    • Theory
    • Text
    • Mathbf
    • Mathcal
    • Displaystyle
    • Schemes
    • One
    • Exact
    • Omega
    • Morphism
    • Definition
    • Flat
  • derived category
    • Functor
    • Object
    • Category
    • Derived
    • Left
    • Given
    • Using
    • Complex
    • Flat
    • First
    • Cotangent
    • One
  • left derived functor
    • Functor
    • Left
    • Category
    • Kähler
    • Object
    • Given
    • Simplicial
    • Differentials
    • Sequence
    • Using
    • Exact
    • First
  • algebraic spaces
    • General
    • Theory
    • Definition
    • Schemes
    • Morphisms
    • Mathcal
    • Spaces
    • Local
    • Morphism
    • Complexes
    • Deformation
    • Exact

Connections between topic areas Semantic bridges

For Cotangent complex, one of the stronger structural bridges in this analysis connects Cotangent complex with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Cotangent complex — Overview · splits 69 ⟂ 22
Cotangent complex — Properties of the cotangent complex · splits 70 ⟂ 21
Cotangent complex — Early work on cotangent complexes · splits 77 ⟂ 14
Cotangent complex — Motivation · splits 78 ⟂ 13
Cotangent complex — The definition of the cotangent complex · splits 84 ⟂ 7
Cotangent complex — Examples · splits 84 ⟂ 7
Cotangent complex — Cotangent complexes in deformation theory · splits 85 ⟂ 6

Map overview Semantic statistics

Cotangent complex

Nodes91
Edges90
Triples105
Avg. degree1.98
Density0.021978
Components1

Source & methodology

TTTA analyzes the structure around Cotangent complex to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Works, Properties of the cotangent complex & Early work on cotangent complexes, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Cotangent complex · EN edition · Analysis: TopicsToTalkAbout

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