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

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6

Fundamental vanishing theorems

There are many important results concerning the vanishing of local cohomology modules. A few results of this type have already been presented earlier in the book: for example, Exercise 1.3.9(iv) is concerned with the fact that, if an R-module M is such that images contains an M-sequence of length n, then images = 0 for all i < n; also, Theorem 3.3.1 shows that, if images can be generated by t elements, then, for every R-module M, we ...

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