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Local cohomology modules of invariant rings
Published online by Cambridge University Press: 18 December 2015
Abstract
Let K be a field and let R be a regular domain containing K. Let G be a finite subgroup of the group of automorphisms of R. We assume that |G| is invertible in K. Let RG be the ring of invariants of G. Let I be an ideal in RG. Fix i ⩾ 0. If RG is Gorenstein then:
(i) injdimRGHiI(RG) ⩽ dim Supp HiI(RG);
(ii) $H^j_{\mathfrak{m}}$(HiI(RG)) is injective, where $\mathfrak{m}$ is any maximal ideal of RG;
(iii) μj(P, HiI(RG)) = μj(P′, HiIR(R)) where P′ is any prime in R lying above P.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 2 , March 2016 , pp. 299 - 314
- Copyright
- Copyright © Cambridge Philosophical Society 2015
References
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