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Explore the main themes, entities and connections around Cotangent complex. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Properties of the cotangent complex
20 related topics
Early work on cotangent complexes
13 related topics
Motivation
Algebraic varietiesExact sequenceRight exact functorAbelian categoryLichtenbaum–Schlessinger functors
12 related topics
Overview
21 related topics
Key facts & relationships
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Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Mathematics
- Cotangent sheaf
- Normal bundle
- Virtual tangent bundle
- Manifolds Manifold
- Schemes Scheme (mathematics)
- Morphism
- Deformation theory Deformation (mathematics)
- Derived category Derived categories
- Sheaves Sheaf (mathematics)
- Homotopical algebra
- Michel André Michel André (mathematician)
- Daniel Quillen
- Commutative rings
- Simplicial Simplicial set
- Left derived functor
- Kähler differentials
- Luc Illusie
- Ringed topoi Ringed topos
- Ringed spaces Ringed space
- Algebraic spaces Algebraic space
Motivation
- Algebraic varieties Algebraic variety
- Exact sequence
- Right exact functor
- Abelian category
- Lichtenbaum–Schlessinger functors Lichtenbaum–Schlessinger functor
- Imperfection modules Imperfection module?action=edit&redlink=1
- Deformation theory
- Derived functor
- Connecting homomorphism
- Conormal exact sequence Conormal exact sequence?action=edit&redlink=1
- Closed immersion
- Formally unramified
Early work on cotangent complexes
- Field extensions Field extension
- Alexander Grothendieck
- Riemann-Roch theorem Grothendieck-Riemann-Roch theorem
- Algebraic geometry
- Virtual tangent bundles Regular embedding
- Pierre Berthelot
- Derived category
- Coherent sheaves Coherent sheaf
- Exact triangle
- Affine schemes Affine scheme
- Gerstenhaber Murray Gerstenhaber
- Lichtenbaum Stephen Lichtenbaum
- Schlessinger Michael Schlessinger
The definition of the cotangent complex
- Homotopical setting Homotopic algebra
- Simplicial commutative rings Simplicial commutative ring
- Topoi Topos
- Simplicial rings Simplicial ring
- Free object
- Model category
Cotangent complexes in deformation theory
Properties of the cotangent complex
- Flat topology
- Localization Localization of a ring
- Étale morphism
- Smooth morphism
- Projective dimension
- Local complete intersection morphism
- Perfect complex
- Regular sequence
- Projective module
- Perfect field
- Noetherian rings Noetherian ring
- André–Quillen homology
- If and only if
- Luchezar Avramov
- Annals Annals of Mathematics
- Bhargav Bhatt Bhargav Bhatt (mathematician)
- Faithfully flat descent
- Faithfully flat morphism
- Homotopy limit
- Amitsur complex
Examples
- Affine space
- Gromov–Witten theory Gromov–Witten invariant
- Algebraic stacks Algebraic stack
- Enumerative geometry
- Complex manifold
- Triangulated categories Triangulated category
Advanced semantic analysis
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Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Cotangent complex
Nodes91
Edges90
Triples105
Avg. degree1.98
Density0.021978
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
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 Word statistics
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Important terminology
displaystyle cotangent complex morphism theory mathbf bullet exact smooth sequence kähler differentials deformation simplicial given algebraic complexes omega morphisms derived
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Cotangent complex | is a | common generalisation of the cotangent sheaf | 0.90 | text |
| Cotangent complex | is a | fact that given a morphism of S | 0.90 | text |
| Cotangent complex | is a | same as the Kähler differentials.Closed embeddings in smooth schemesLet i | 0.90 | text |
| Cotangent complex | is a | same as the Kähler differentials | 0.90 | text |
| manifolds or schemes | instance of | normal bundle and virtual tangent bundle of a map of geometric spaces | 0.80 | text |
| Cotangent complex | related to Characterization of local complete intersections | The | 0.60 | section |
| Cotangent complex | related to Characterization of local complete intersections | Let | 0.60 | section |
| Cotangent complex | related to Characterization of local complete intersections | A-algebra | 0.60 | section |
| Cotangent complex | related to Characterization of local complete intersections | As | 0.60 | section |
| Cotangent complex | related to Characterization of local complete intersections | Quillen | 0.60 | section |
| Cotangent complex | related to Characterization of local complete intersections | Lichtenbaum | 0.60 | section |
| Cotangent complex | related to Characterization of local complete intersections | Schlessinger | 0.60 | section |
No triples extracted yet.
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