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Definition 48.24.1. Let $X$ be a scheme. We say $X$ is Gorenstein if $X$ is locally Noetherian and $\mathcal{O}_{X, x}$ is Gorenstein for all $x \in X$.

Comments (2)

Comment #1293 by Liran Shaul on

I think this definition is somewhat nonstandard: it rules out Gorenstein rings of infinite Krull dimension, and there are known examples of such rings (usually Gorenstein is defined to be a ring such that is a local Gorenstein ring for all ). A discussion about this can be found here:

http://mathoverflow.net/questions/23240/is-there-a-non-gorenstein-ring-but-locally-gorenstein

There are also:

  • 4 comment(s) on Section 48.24: Gorenstein schemes

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View Definition 48.24.1 as pdf