Coherent Sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometrical information. In addition, there is a related concept of quasi-coherent sheaves. Many results and properties in algebraic geometry and complex analytic geometry are formulated in terms of coherent sheaves and their cohomology.
Coherent sheaves can be seen as a generalization of (sheaves of sections of) vector bundles. They form a category closed under usual operations such as taking kernels, cokernels and finite direct sums. In addition, under suitable compactness conditions they are preserved under maps of the underlying spaces and have finite dimensional cohomology spaces.
Read more about Coherent Sheaf: Definition, Examples of Coherent Sheaves, Coherent Cohomology
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