It is well known that an affine scheme $X=\mathrm{Spec}(A)$ is quasi compact. In analogy, what can we say about an affine formal scheme $\mathrm{Spf}(A)$ (here $A$ should be an adic ring and $\mathrm{Spf}(A)$ is defined to be the set of all open primes in $A$ with respect to the adic topology)? Is it also quasi-compact? If the answer is no, what additional conditions can guarantee the quasi-compactness?
2026-03-25 06:11:11.1774419071
Is an affine formal scheme quasi-compact?
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