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Local Cohomology, Second Edition by R. Y. Sharp, M. P. Brodmann

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5

Other approaches

Although we have now developed enough of the basic algebraic theory of local cohomology so that we could, if we wished, start right away with serious calculations with local cohomology modules, there are two other approaches to the construction of local cohomology modules which are useful, and popular with many workers in the subject. One approach uses cohomology of Čech complexes, and the other uses direct limits of homology modules of Koszul complexes. Links between local cohomology and Koszul complexes and Čech cohomology are described in A. Grothendieck’s foundational lecture notes [25, §2]; related ideas are present in J.-P. Serre’s fundamental paper [77, §61]. Among other texts which discuss links between local cohomology ...

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