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In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf.

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rdfs:label	Coherent sheaf (en) Kohärente Garbe (de) 連接層 (ja) 연접층 (ko) Когерентный пучок (ru) 凝聚層 (zh)
rdfs:comment	In den mathematischen Teilgebieten der algebraischen Geometrie und komplexen Analysis sind kohärente Garben das Analogon endlich erzeugter Moduln über noetherschen Ringen. (de) 数学では、特に代数幾何学や複素多様体やスキームの理論では、連接層(れんせつそう、英: coherent sheaf)とは、底空間の幾何学的性質に密接に関連する、扱いやすい性質をもった特別な層である。連接層は有限ランクのベクトルバンドルや局所自由層の一般化とみなすことができる。ベクトルバンドルとは違い、連接層のなす圏は、や余核や有限の直和といった操作で閉じている｢素晴らしい｣圏である。準連接層(じゅんれんせつそう、英：quasi-coherent sheaf)は連接層における有限性の仮定をはずしたもので、ランク無限の局所自由層を含んでいる。代数幾何学や複素解析の多くの結果や性質が、連接層、準連接層やそれらのコホモロジーのことばで定式化される。 (ja) 在數學中，尤其是代數幾何與複流形理論裡，凝聚層是一類特別容易處理的層。凝聚層的定義指涉到一個環層（例如一個概形的結構層、複流形上的全純函數層或），此環層蘊藏了所論空間的幾何性質。相關的概念還有擬凝聚層與有限展示層。代數幾何與複解析幾何裡的許多性質與定理都以凝聚層及其上同調表述。凝聚層可被視作向量叢截面層的推廣。它們構成的範疇在取核、上核、有限直和等操作下封閉。此外，若底空間滿足合宜的緊緻條件，則凝聚性在底空間的映射下保持不變，且具有有限維的群。交換代數裡的一些定理也能應用於凝聚層，如中山正引理。 (zh) In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf. (en) 대수기하학과 복소기하학에서 연접 가군층(連接加群層, 영어: coherent sheaf of modules, 프랑스어: faisceau de modules cohérent) 또는 단순히 연접층(連接層)은 유한 계수 벡터 다발(국소 자유층)의 핵 · 여핵으로 구성할 수 있는 가군층이다. 연접 가군층은 벡터 다발과 마찬가지로 공간의 기하학적 성질과 밀접하게 연관된 좋은 성질을 가지며, 카르탕 정리나 가가 정리 등 대수기하학과 복소해석기하학에서의 여러 정리가 성립한다. 이 경우, 는 부분 공간 위에만 존재하는 "벡터 다발"이며, 는 부분 공간 위에만 존재하는 "벡터 다발"이다. 이와 같이 "부분 공간 위의 벡터 다발"을 허용하여 유한 차원 벡터 다발의 범주를 더 확장시켜 얻는 아벨 범주를 생각해 볼 수 있다. 이러한 아벨 범주는 존재하며, 그 원소를 연접 가군층이라고 한다. (ko) Когерентные пучки — класс пучков, тесно связанных с геометрическими свойствами пространства-носителя.В определении когерентного пучка используется пучок колец, который хранит эту геометрическую информацию. Когерентные пучки можно рассматривать как обобщение векторных расслоений. В отличие от векторных расслоений, они образуют абелеву категорию, и поэтому замкнуты относительно таких операций, как взятие ядер, коядер и образов. Квазикогерентные пучки — это обобщение когерентных пучков, включающее в себя векторные расслоения бесконечного ранга. (ru)
dct:subject	Complex manifolds Topological methods of algebraic geometry Vector bundles Algebraic geometry Sheaf theory
Wikipage page ID	603780 (xsd:integer)
Wikipage revision ID	1123109714 (xsd:integer)
Link from a Wikipage to another Wikipage	Quasi-compact Morphism of schemes Determinant line bundle Algebraic K-theory Complex manifolds Ricci curvature Volume form Kähler differential Affine scheme Ringed space Quasi-coherent sheaf on an algebraic stack Essentially finite vector bundle Chow ring Normal bundle Tangent bundle Quotient of an abelian category Full subcategory Equivalence of categories Localization of a module Projective scheme Topological methods of algebraic geometry Linear algebra Short exact sequence Closed immersion Complex manifold Ideal sheaf Picard group Bundle of principal parts Vector bundles Gabriel–Rosenberg reconstruction theorem Sheaf of modules Algebraic geometry Algebraic variety Ample line bundle Exterior power Field (mathematics) Finitely generated module Flat module Diagonal morphism Direct sum Fano variety Graded ring Graduate Texts in Mathematics Ofer Gabber Projective module Proper morphism Resolution (algebra) Jean-Pierre Serre Cotangent bundle Tensor product Abelian category Abelian variety Algebraic geometry Sheaf theory Chern class K3 surface Kernel (category theory) Coherent sheaf cohomology Cokernel Hodge theory Homogeneous polynomial Tautological line bundle Regular scheme

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