Graded Greenlees-may Duality and the Čech Hull
نویسنده
چکیده
The duality theorem of Greenlees and May relating local cohomology with support on an ideal I and the left derived functors of I-adic completion [GM92] holds for rather general ideals in commutative rings. Here, simple formulas are provided for both local cohomology and derived functors of Z-graded completion, when I is a monomial ideal in the Z-graded polynomial ring k[x1, . . . , xn]. Greenlees-May duality for this case is a consequence. A key construction is the combinatorially defined Čech hull operation on Z-graded modules [Mil98, Mil00, Yan00]. 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.
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