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

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14

Graded versions of basic theorems

We have now laid the foundations of multi-graded local cohomology theory in Chapter 13, where the gradings on R and R-modules M are by a finitely generated, torsion-free Abelian group G. Indeed, in the case where R is G-graded and the ideal image is G-graded, we now know that, for a G-graded R-module M, there is a natural way in which to define G-gradings on the local cohomology modules image(M) (iimage0); furthermore, whenever ...

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