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I am about to create D-scheme, but currently the Lab is down and the server does not react to my login attempts…
okay, I have created an entry D-scheme
There is such an entry already! In a variant, diffiety. See also D-geometry, and especially crystal.
Okay. You need to remember including the relevant redirects when you create an entry! I’ll inlcude them now.
Well, I am not sure. Maybe we indeed want to have D-scheme separate from diffiety. It is almost the same, but formally not entirely. I had that in mind then. But I stopped the activity on the D-geometry at the time, abruptly because there was no support/interest from the rest of the n-community at the time.
Edit: why did you add toc for higher geometry – this is a notion of 1-categorical algebraic geometry. It can be viewed higher categorical, but it is optional. I would be much happier to consider it part of the cluster D-geometry as most of the practioners (cited references) do.
I have kept the entries separately, just cross-linked them.
I had already renamed the toc to just “Geometry”. We just have a single such toc. I used to call it “Higher geoemtry”, but it should just be called “Geometry”.
Around here everything is higher by default
Still, I will once replace this by lower circle D-geometry once. It is more closely related circle, but I have abosolutely no time to work tyhese days on it.
Ah, Thanks. I know Lurie’s notes, but apparently I didn’t read them thoroughly.
So I was proud to have figured out that the Jet scheme is just the change of base along the de Rham space projection. But sure enough that’s what Lurie says on p. 6 there. Thanks.
You know, now that it is officially not my original idea, I can tell you my opinion about it without being constrained by modesty: this is great! :-) This is way better than what BD write. This makes D-geometry entirely general abstract and work in vast generality away from the original examples.
I have added to D-scheme pointers to Lurie’s statement/proof of the assertion that $\mathcal{D}_X$-schemes are just schemes over $\mathbf{\Pi}_{inf}(X)$.
This looks like somewhat related to the relative connections in the sense of p-connection. The idea of jet scheme as a crystal of schemes is I think from Grothendieck’s work on de Rham cohomology for alegbraic varieties. About de Rham space there is also fundamental idea in a paper of Kapranov in late 1980s where he had the idea for categories of complexes.
I am not user if I remember right but I think it is about this article
I have the article, but I am not very familiar with it, I looked just at few related details at the time when I looked at that subject.
Edit: after taking a look, maybe not quite that. Some other apsects related to the subject.
This makes D-geometry entirely general abstract and work in vast generality away from the original examples.
It makes sense whenever you have a resolution of diagonal.
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