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Is there a name for the standard sheaf $\mathscr{O}$ on $\operatorname{Spec}A$ defined to be the set of locally constant functions to the localizations of $A$ ? It is used so often but I don't know the name for it. "Structure sheaf" seems slightly more general than what I'm looking for.

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    @ashpool Of course not. Let $k$ be any field, then $\operatorname{Spec} k[x]_{(x)}$ is the Sierpiński space – for any choice of $k$.2012-08-13

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