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Tim Campion
3:58 AM
@HarryGindi Riehl and Verity also have a treatment of straightening / unstraightening
5 hours later…
Harry Gindi
8:29 AM
@TimCampion It's not finished yet. It's not proven to be functorial
14 hours later…
Elden Elmanto
10:06 PM
@DenisNardin I learned from a masterpiece
numdam.org/item/BSMF_2010__138_2_181_0
that the Zariski+constructible+"S-topology" (defined in terms of generizations and specializations) makes the Zariski topology truly geometric :)
Denis Nardin
@EldenElmanto This seems interesting. Can you elaborate? I thought that Zariski=constructible+S-topology
In fact this is true more generally in spectral spaces, or stably compact spaces
Elden Elmanto
@DenisNardin Right. I should say thinking of Zar=cbl + S is really an aid to think about how the zariski topology looks like on a scheme.
Denis Nardin
In fact it's even better: the category of spectral spaces and spectral map is equivalent to the category of posets in Stone spaces
Elden Elmanto
For example Cor 2.9 rephrases universal epis in terms of these valuation rings and the idea uses Zar = cbl + S
Denis Nardin
Yeah, I like these things a lot :).
Elden Elmanto
10:15 PM
I know. It's lovely :)
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