The quasi-coherent sheaves are a generalization of coherent sheaves and include the locally free sheaves of infinite rank. Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf. Definitions A ... 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 • 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, … 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 … See more For a morphism of schemes $${\displaystyle X\to Y}$$, let $${\displaystyle \Delta :X\to X\times _{Y}X}$$ be the diagonal morphism, which is a closed immersion if $${\displaystyle X}$$ is separated over $${\displaystyle Y}$$. Let See more A quasi-coherent sheaf on a ringed space $${\displaystyle (X,{\mathcal {O}}_{X})}$$ is a sheaf $${\displaystyle {\mathcal {F}}}$$ of $${\displaystyle {\mathcal {O}}_{X}}$$ See more On an arbitrary ringed space quasi-coherent sheaves do not necessarily form an abelian category. On the other hand, the quasi-coherent sheaves on any scheme form an abelian category, and they are extremely useful in that context. On any ringed space See more An important feature of coherent sheaves $${\displaystyle {\mathcal {F}}}$$ is that the properties of $${\displaystyle {\mathcal {F}}}$$ at … See more WebAug 27, 2024 · An interesting in-depth comparison of the notions of quasi-coherent sheaves in commutative and noncommutative context are also in Orlov’s article quoted above. The …
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WebApr 8, 2024 · 3. Let f: X → Y be an affine morphism. Prove that the direct image sheaf f ∗ O X is a quasi-coherent O Y -module. One of the equivalent definitions of a quasi-coherent O X … WebApr 13, 2024 · Classifying finite localizations of quasi-coherent sheaves. 作者: Grigory Garkusha . 来自arXiv 2024-04-13 17:39:27. 0. 0. 0. office word excel powerpoint gratuit
Prove that sheaf is quasi-coherent - Mathematics Stack Exchange
WebApr 11, 2024 · The Zariski cohomology is just ordinary sheaf cohomology. The latter one commutes with colimits of coherent and sober spaces with quasi-compact transition maps [15, ch. 0, 4.4.1]. Since the admissible Zariski-Riemann space is such a colimit we obtain WebThen, the kernel J of i # is a quasi-coherent ideal sheaf, and i induces an isomorphism from Z onto the closed subscheme defined by J. [1] A particular case of this correspondence is … Web3. If S;T are coherent sheaves over a variety X, give an example to show that the presheaf U ÞÑSpUqb OpUqTpUqneed not be a sheaf. (The tensor product S bT is de ned to be its shea cation.) 4. If M;~ N~ are quasi-coherent over an a ne X with OpXq R, then M~ bN~ M…b R N. 5. For S;T quasi-coherent over X Qx, the stalks satisfy pS bTq x S x b O ... office word et excel