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

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Preface to the First Edition

One can take the view that local cohomology is an algebraic child of geometric parents. J.-P. Serre’s fundamental paper ‘Faisceaux algébriques cohérents’ [77] represents a cornerstone of the development of cohomology as a tool in algebraic geometry: it foreshadowed many crucial ideas of modern sheaf cohomology. Serre’s paper, published in 1955, also has many hints of themes which are central in local cohomology theory, and yet it was not until 1967 that the publication of R. Hartshorne’s ‘Local cohomology’ Lecture Notes [25] (on A. Grothendieck’s 1961 Harvard University seminar) confirmed the effectiveness of local cohomology as a tool in local algebra.

Since the appearance of the Grothendieck–Hartshorne notes, local ...

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