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16
votes
Accepted
Locales as spaces of ideal/imaginary points
I can only answer some of your questions.
Yes, the Zariski locale is extensively studied. It's one of the ways of setting up scheme theory in a constructive context: Don't define schemes as locally r …
8
votes
Accepted
Points of the big Zariski site
Let's simplify and consider the presheaf topos.
I asked the same question over at the nForum a while back. There Marc Hoyois reminded me of the following quite general fact: The category of topos-the …