Scholars@Duke publication: Graded greenlees-may duality and the cech hull

Local Cohomology and Its Applications

Graded greenlees-may duality and the cech hull

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Miller, E

January 1, 2001

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.

Duke Scholars

Author Ezra Miller Mathematics

Publication Date

January 1, 2001

Start / End Page

233 / 253

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Miller, E. (2001). Graded greenlees-may duality and the cech hull. In Local Cohomology and Its Applications (pp. 233–253).

Miller, E. “Graded greenlees-may duality and the cech hull.” In Local Cohomology and Its Applications, 233–53, 2001.

Miller E. Graded greenlees-may duality and the cech hull. In: Local Cohomology and Its Applications. 2001. p. 233–53.

Miller, E. “Graded greenlees-may duality and the cech hull.” Local Cohomology and Its Applications, 2001, pp. 233–53.

Miller E. Graded greenlees-may duality and the cech hull. Local Cohomology and Its Applications. 2001. p. 233–253.

Publication Date

January 1, 2001

Start / End Page

233 / 253