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Explore the main themes, entities and connections around D-module. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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D-modules on algebraic varieties
27 related topics
Holonomic modules
21 related topics
Applications
7 related topics
Overview
24 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
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
- Module Module (mathematics)
- Ring Ring (mathematics)
- Differential operators Differential operator
- Linear partial differential equations Linear partial differential equation
- Mikio Sato
- Algebraic analysis
- Joseph Bernstein
- Bernstein–Sato polynomial
- Masaki Kashiwara
- Sheaf theory
- Alexander Grothendieck
- Algebraic geometry
- Functional analysis
- Over-determined systems Over-determined system
- Holonomic systems Holonomic system
- Characteristic variety
- Symbols Symbol of a differential operator
- Lagrangian submanifold
- Cotangent bundle
- Involutive systems Involutive system
- Zoghman Mebkhout
- Derived category
- Riemann–Hilbert correspondence
Modules over the Weyl algebra
- Weyl algebra
- Field Field (mathematics)
- Characteristic Characteristic (algebra)
- Commutator
- Left module
- Polynomial ring
- Partial differentiation
- Holomorphic function
- Vector space
D-modules on algebraic varieties
- Smooth Smooth morphism
- Algebraic variety
- Sheaf Sheaf (mathematics)
- Vector fields Vector field
- Derivations Differential algebra
- Action Group action (mathematics)
- Leibniz rule Product rule
- Vector bundle
- Connection Connection (vector bundle)
- Equivalence of categories
- Tensor product
- Line bundle
- Exterior power
- Differential 1-forms Differential form
- Lie derivative
- System of coordinates Regular system of parameters
- Tangent space
- Regular functions Regular function
- Affine space
- Coherent sheaves Coherent sheaf
- Locally free sheaf
- Pullback and pushforward functors Image functors for sheaves
- Map Morphism of schemes
- Chain rule
- Right exact Right exact functor
- Derived functor
- Homological algebra
Holonomic modules
- Noetherian ring
- Simple Simple ring
- Ideals Ideal (algebra)
- Zero ideal
- Commutative algebra
- Hilbert polynomial
- Length Length of a module
- Filtration Filtration (algebra)
- Multiindex notation
- Graded ring
- Finitely generated Finitely generated module
- Artin–Rees lemma
- Numerical polynomial
- Order of differential operators Order of a differential operator
- Radical Radical of an ideal
- Annihilator Annihilator (ring theory)
- Closed immersion
- Verdier duality
- Regular rings Regular ring
- Global homological dimension
- Symplectic geometry
Applications
Bibliography
- Beilinson, A. A. Alexander Beilinson
- ISSN ISSN (identifier)
- MR MR (identifier)
- ISBN ISBN (identifier)
- Inventiones Mathematicae
- Bibcode Bibcode (identifier)
- Doi Doi (identifier)
- S2CID S2CID (identifier)
- Cambridge University Press
- Borel, Armand Armand Borel
- Academic Press
- Encyclopedia of Mathematics
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.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.D-module
Nodes107
Edges106
Triples133
Avg. degree1.98
Density0.018692
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.
D-module
Top relations
related to Bibliography · 50
D-module → Academic Press, Académie, Algebraic D-Modules, Amsterdam, Armand, Beilinson, Bernstein, BF01389272, Bibcode, Birkhäuser Boston, Boston, Cambridge University Press, Comptes Rendus, D-modules, Doorn, EMS PressHotta, Encyclopedia, Inventiones Mathematicae, ISBN, ISSN
related to Holonomic modules over the Weyl algebra · 20
D-module → An, Artin, Bernstein, D-modules, DX, Finitely, FpAn, Hilbert, In, It, K-linear, More, Moreover, Noetherian, Notably, Rees, The, The Hilbert, These, Weyl
related to External links · 11
D-module → Algebraic, Algebraic Theory, Bernstein, D-modules, Dennis, Dragan, Gaitsgory, Geometric Representation Theory, Joseph, Lectures, PDF
related to D-modules on algebraic varieties · 8
D-module → D-modules, DX, DX-module, Giving, K-linear, OX-algebra, OX-module, The
related to Geometric representation theory · 7
D-module → Beilinson, Bernstein, D-modules, G/B, It, Langlands, Lie
related to Functoriality · 6
D-module → D-modules, DX, DY, For, The, This
related to General definition · 6
D-module → As, D-modules, DX, The, The Bernstein, Weyl
related to Modules over the Weyl algebra · 5
D-module → An, D-modules, It, The, Weyl
related to Properties and characterizations · 5
D-module → Also, For, Holonomic, K-vector, Li
has application · 4
D-module → Bernstein, D-modules, One, Sato
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
d-modules differential holonomic algebraic theory dx algebra ring left bernstein module polynomial bundle modules weyl hilbert defined right operators characteristic
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 |
|---|---|---|---|---|
| D-module | is a | module over a ring D of differential operators | 0.90 | text |
| Hilbert polynomial | instance of | standard notions from commutative algebra | 0.80 | text |
| multiplicity | instance of | standard notions from commutative algebra | 0.80 | text |
| length of modules carry over to D-modules | instance of | standard notions from commutative algebra | 0.80 | text |
| D-module | has application | One | 0.60 | section |
| D-module | has application | D-modules | 0.60 | section |
| D-module | has application | Bernstein | 0.60 | section |
| D-module | has application | Sato | 0.60 | section |
| D-module | related to Bibliography | Lock-green | 0.60 | section |
| D-module | related to Bibliography | Lock-gray-alt-2 | 0.60 | section |
| D-module | related to Bibliography | Lock-red-alt-2 | 0.60 | section |
| D-module | related to Bibliography | Wikisource-logo | 0.60 | section |
No triples extracted yet.
Related concept clusters Concept neighborhoods
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Connections between topic areas Semantic bridges
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