Definition 111.27.2. We define the homogeneous spectrum $\text{Proj}(R)$ of the graded ring $R$ to be the set of homogeneous, prime ideals ${\mathfrak p}$ of $R$ such that $R_{+} \not\subset {\mathfrak p}$. Note that $\text{Proj}(R)$ is a subset of $\mathop{\mathrm{Spec}}(R)$ and hence has a natural induced topology.
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