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

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8

The Lichtenbaum–Hartshorne Theorem

In this chapter, we take up again the main theme of Chapter 6, and establish another vanishing theorem for local cohomology modules, namely the local Lichtenbaum–Hartshorne Vanishing Theorem (see R. Hartshorne [29, Theorem 3.1], and C. Peskine and L. Szpiro [66, chapitre III, théorème 3.1]). While two important vanishing theorems in Chapter 6, namely Grothendieck’s Vanishing Theorem 6.1.2, and Theorem 6.2.7, which shows that, for a finitely generated R-module M such that imageMM, we have image(M) = 0 for all i < grade ...

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