WebJul 8, 2024 · The notion of coherent sheaf, as defined in EGA, is not functorial, that is, pullbacks of coherent sheaves are not necessarily coherent. Hartshorne’s book defines … Web2. Finiteness conditions on quasicoherent sheaves: nite type quasicoherent sheaves, and coherent sheaves 3 3. Coherent modules over non-Noetherian rings ?? 6 4. Pleasant properties of nite type and coherent sheaves 8 1. MODULE-LIKE CONSTRUCTIONS In a similar way, basically any nice construction involving modules extends to quasico-herent …
Coherent sheaf - Wikipedia
WebIn mathematics, a semiorthogonal decomposition is a way to divide a triangulated category into simpler pieces. One way to produce a semiorthogonal decomposition is from an exceptional collection, a special sequence of objects in a triangulated category.For an algebraic variety X, it has been fruitful to study semiorthogonal decompositions of the … WebOn a noetherian scheme the notions of finitely presented and coherent sheaves of O-modules agree, but this is not true on a general scheme or general analytic space; … ground cover plants ready to plant
Coherent sheaf - Wikiwand
WebWe develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi- coherent sheaves, and the di erence becomes crucial for the formulation of the categorical Geometric Langlands Correspondence. Contents Introduction 3 0.1. Weberations one might perform on sheaves are described in paragraph 1; we follow quite exactly the exposition of Cartan ([2], [5]). In paragraph 2 we study co-herent sheaves of modules; these generalize analytic coherent sheaves (cf. [3], [5]), admitting almost the same properties. Paragraph 3 contains the de nition Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under operations such as taking kernels, images, and cokernels. The quasi-coherent sheaves are a generalization of coherent sheaves and include the locally free … See more 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 … See more On an arbitrary ringed space quasi-coherent sheaves do not necessarily form an abelian category. On the other hand, the quasi-coherent … See more Let $${\displaystyle f:X\to Y}$$ be a morphism of ringed spaces (for example, a morphism of schemes). If $${\displaystyle {\mathcal {F}}}$$ is a quasi-coherent sheaf on $${\displaystyle Y}$$, then the inverse image $${\displaystyle {\mathcal {O}}_{X}}$$-module … See more For a morphism of schemes $${\displaystyle X\to Y}$$, let $${\displaystyle \Delta :X\to X\times _{Y}X}$$ be … See more A quasi-coherent sheaf on a ringed space $${\displaystyle (X,{\mathcal {O}}_{X})}$$ is a sheaf $${\displaystyle {\mathcal {F}}}$$ of $${\displaystyle {\mathcal {O}}_{X}}$$-modules which … See more • An $${\displaystyle {\mathcal {O}}_{X}}$$-module $${\displaystyle {\mathcal {F}}}$$ on a ringed space $${\displaystyle X}$$ is called locally free of finite rank, or a vector bundle, if every point in $${\displaystyle X}$$ has an open neighborhood $${\displaystyle U}$$ such … See more An important feature of coherent sheaves $${\displaystyle {\mathcal {F}}}$$ is that the properties of $${\displaystyle {\mathcal {F}}}$$ at a point $${\displaystyle x}$$ control the behavior of $${\displaystyle {\mathcal {F}}}$$ in a neighborhood of $${\displaystyle x}$$, … See more filip marco winery