I'm not sure that this is generally true, but Harthorne p73 seems to suggest it. If it is true could someone give me a hint for the proof?
2026-04-09 13:21:56.1775740916
If $f$ an isomorphism of ringed spaces, is $f$ necessarily an isomorphism of locally ringed spaces?
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Yes. See Stacks project, (21.2.2).