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Let $(R,m,k)$ be a (noetherian) regular local ring of depth=dimension $d$, and let $D$ be a dualizing module for $R$ (say, the injective envelope of $R/m$).

Then is $D_p$ dualizing for $R_p$ for any prime $p$ of $R$ (more generally, if $R$ is Gorenstein and $p$ is a prime such that $R_p$ is also Gorenstein)? If it is true, could I have a reference for a proof?

Bump!

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    it may be time to ask your question on Math Overflow.2011-03-22
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    @Pete L. Clark: I found out that this is actually true. It's an exercise in section 9.5 (9.6 maybe; the section on local duality anyhow) in Enochs _Relative homological algebra_, but I'm still not sure on how to prove it.2011-03-22
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    See for example, Hartshorne - Residues and duality, Chapter V, Corollary 2.3 for a proof that being a dualizing complex is a local property.2011-04-27

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