Given an affine variety, which is defined to the vanishing set $V(I)$ over an algebraic field $k$. We know its coordinate ring $A(Y)$ has the property that $\mathcal{O}(Y)\cong A(Y)$. I wonder if we have that $(Y,\mathcal{O}_Y)\cong (\operatorname{Spec}(A(Y)),\mathcal{O}_{A(Y)}) $ so that $Y$ is an affine scheme?
2026-03-25 16:08:22.1774454902
$(Y,\mathcal{O}_Y)\cong (\operatorname{Spec}(A(Y)),\mathcal{O}_{A(Y)}) $?
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