Rings with a Local Cohomology Theorem and Applications to Cohomology Rings of Groups
نویسندگان
چکیده
Cohomology rings of various classes of groups have curious duality properties expressed in terms of their local cohomology [2, 3, 12, 4, 5, 6]. We formulate a purely algebraic form of this duality, and investigate its consequences. It is obvious that a Cohen-Macaulay ring of this sort is automatically Gorenstein, and that its Hilbert series therefore satisfies a functional equation, and our main result is a generalization of this to rings with depth one less than their dimension: this proves a conjecture of Benson and Greenlees [4]
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تاریخ انتشار 1999