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.
Terminology for the sheaf on Spec A
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algebraic-geometry
sheaf-theory
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0@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