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In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and Joseph Bernstein on the Bernstein–Sato polynomial.

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rdf:type	software yago:WikicatPartialDifferentialEquations yago:Abstraction100002137 yago:Communication100033020 yago:DifferentialEquation106670521 yago:Equation106669864 yago:MathematicalStatement106732169 yago:Message106598915 yago:PartialDifferentialEquation106670866 yago:Statement106722453
rdfs:label	D-module (en) D-module (fr) D가군 (ko) D-加群 (ja)
rdfs:comment	En mathématiques, un D-module est un module sur un anneau D d'opérateurs différentiels. L'intérêt principal des D-modules réside en son utilisation dans l'étude d'équations aux dérivées partielles. (fr) 수학에서 D가군(영어: D-module)은 미분 연산자들의 환에 대한 가군층이다. 선형 편미분 방정식의 추상화이며, 또한 평탄한 코쥘 접속을 갖춘 벡터 다발의 일반화이다. (ko) 数学において、D-加群(D-module)は、微分作用素の環 D 上の加群である。そのような D-加群への主要な興味は、の理論へのアプローチとしてである。1970年ころ以来、D-加群の理論は、主要には代数解析上の佐藤幹夫のアイデアのまとめて、についての佐藤とヨゼフ・ベルンシュタイン(Joseph Bernstein)の仕事へと発展した。初期の主要な結果は、柏原正樹のとである。D-加群論の方法は、常に、層の理論から導かれ、代数幾何学のアレクサンドル・グロタンディークの仕事からに動機を得たテクニックを使った。D-加群のアプローチは、微分作用素を研究する伝統的な函数解析のテクニックとは異なっている。最も強い結果は、（）に対して得られ、表象によりが定義される。特性多様体は余接バンドルの包合的部分集合であり，その中で最良の例が、最小次元の余接バンドルのラグラジアン部分多様体である（）。テクニックは、グロタンディーク学派の側からゾグマン・メブク (Zoghman Mebkhout) により開発された。彼は、すべての次元でのの導来圏の一般的なバージョンを得た。 (ja) In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and Joseph Bernstein on the Bernstein–Sato polynomial. (en)
dcterms:subject	Algebraic analysis Partial differential equations Sheaf theory
Wikipage page ID	3440755 (xsd:integer)
Wikipage revision ID	1117732931 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Beilinson–Bernstein localization Product rule Module (mathematics) Morphism of schemes Algebraic analysis Algebraic analysis Joseph Bernstein Right exact functor Characteristic variety Vector field Derived category Derived functor Inventiones Mathematicae Lie derivative Commutator Masaki Kashiwara Mathematics Noetherian ring Connection (vector bundle) Equivalence of categories Annihilator (ring theory) Bernstein–Sato polynomial Left module Lie algebra Closed immersion Commutative algebra Functional analysis Tangent space Weyl algebra Line bundle Perverse sheaf Riemann–Hilbert correspondence Affine space Alexander Grothendieck Algebraic geometry Algebraic variety Exterior power Field (mathematics) Finitely generated module Differential operator Graded ring Length of a module Radical of an ideal Regular function Regular ring Ring (mathematics) Group action (mathematics) Cotangent bundle Tensor product Partial differential equations Academic Press Sheaf theory Chain rule Characteristic (algebra) Symplectic geometry Coherent sheaf Homological algebra Reductive group Differential algebra Differential form Artin–Rees lemma Polynomial ring Zero ideal Mikio Sato Sheaf (mathematics) Vector bundle Image functors for sheaves Lagrangian submanifold Symbol of a differential operator Multiindex notation Verdier duality Simple ring Smooth morphism Zoghman Mebkhout Involutive system Linear partial differential equation

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