Definition:Structure Sheaf of Spectrum of Ring
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Definition
Let $A$ be a commutative ring with unity.
Let $\struct {\Spec A, \tau}$ be its spectrum with Zariski topology $\tau$
Definition 1
Note that Principal Open Subsets form Basis of Zariski Topology on Prime Spectrum.
We define the structure sheaf of $\Spec A$ to be the sheaf induced by a sheaf on this basis defined as follows:
- For $f \in A$, $\map \OO {\map X f}$ is the localization of $A$ at $f$
- For $f, g \in A$ with $\map X f \supset \map X g$, the restriction is the induced homomorphism of $A$-algebras $A_f \to A_g$.
Definition 2
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Definition 3
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