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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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Under the condition specified below, is $\mathcal{O}_X(X-V(I))=R$, where $X=\mathrm{Spec}R$?
Is it true that given a noetherian normal domain $R$ and an ideal $I$ of height $\geq 2$ we have $\mathcal{O}_X(X-V(I))=R$, where $X=\mathrm{Spec}R$?
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textbooks on modern algebraic geometry for 21st-century starters
As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks?
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