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

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20

Links with sheaf cohomology

In this last chapter we shall develop the links between local cohomology and the cohomology of quasi-coherent sheaves over certain Noetherian schemes. Here we shall assume for the first time that the reader has some basic knowledge about schemes and sheaves: our reference for these topics is Hartshorne’s book [30]. The central idea in this chapter is to extend our earlier relations in 2.3.2 and 15.1.3 between ideal transforms and rings of regular functions on varieties to quasi-coherent sheaves over certain Noetherian schemes. We shall be very concerned with a generalization of the ‘Deligne Isomorphism’ (see [30, Chapter III, Exercise 3.7, p. 217]) which links the group of sections (over an open subset) of an induced ...

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