Rings with a local cohomology theorem and applications to cohomology rings of groups

J. P.C. Greenlees, G. Lyubeznik

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Cohomology rings of various classes of groups have curious duality properties expressed in terms of their local cohomology (Benson and Carlson, Trans. Amer. Math. Soc. 342 (1994) 447-488; Bull. London Math. Soc. 26 (1994) 438-448; Greenlees, J. Pure Appl. Algebra 98 (1995) 151-162; Benson and Greenlees, J. Pure Appl. Algebra 122 (1997) 41-53, J. Algebra 192 (1997) 678-700; Symonds, in preparation). 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 (1997).

Original languageEnglish (US)
Pages (from-to)267-285
Number of pages19
JournalJournal of Pure and Applied Algebra
Volume149
Issue number3
DOIs
StatePublished - Jun 6 2000

Bibliographical note

Funding Information:
(This work began whilst the second author was visiting She eld, supported by a Visiting Fellowship from the EPSRC. ∗Corresponding author. E-mail addresses: j.greenlees@she eld.ac.uk (J.P.C. Greenlees), gennady@math.umn.edu (G. Lyubeznik).

Fingerprint

Dive into the research topics of 'Rings with a local cohomology theorem and applications to cohomology rings of groups'. Together they form a unique fingerprint.

Cite this