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

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18

Applications to reductions of ideals

Graded local cohomology theory has played a substantial rôle in the study of Rees rings and associated graded rings of proper ideals in local rings. We do not have enough space in this book to include all we would like about the applications of local cohomology to this area, and so we have decided to select a small portion of the theory which gives some idea of the flavour. The part we have chosen to present in this chapter concerns links between the theory of reductions of ideals in local rings and the concept of Castelnuovo regularity, discussed in Chapter 16. The highlight will be a theorem of L. T. Hoa which asserts that, if b is a proper ideal in a local ring having infinite residue field, then there ...

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