Graded greenlees-may duality and the cech hull
© 2002 by Taylor and Francis Group, LLC. The duality theorem of Greenlees and May relating local cohomology with support on an ideal I and the left derived functors of J-adic completion [GM92) holds for rather general ideals in commutative rings. Here, simple formulas are provided for both local cohomology and derived functors of zn-graded completion, when I is a monomial ideal in the Zn-graded polynomial ring k[xl,…, xn] Greenlees-May duality for this case is a consequence. A key construction is the combinatorially defined Cech hull operation on Zn-graded modules [Mil98, MilOO, YanOO]. A simple self-contained proof of GM duality in the derived category is presented for arbitrarily graded noetherian rings, using methods motivated by the Čech hull.
- Local Cohomology and its Applications
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International Standard Book Number 13 (ISBN-13)