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Paul VanKoughnett
Paul VanKoughnett
03:08
Does anyone know a good reference for deformations of finite flat commutative group schemes? I specifically care about the p-torsion of a finite height formal group -- does it have a universal deformation, and if not, how are its deformations related to the deformations of the formal group?
 
11 hours later…
Tomer Schlank
Tomer Schlank
14:37
Given a small infinity category C we have a functor A: PSh(C) \to Cat_00 that sends a presheaf F \in PSh(C) to the pullback C \times_{PSh(C)} PSh(C)_{/F}. I would like to have a reference showing that A is colimit preserving.
A reference that identifies A with unstraightening would also suffice.
 
1 hour later…
Harry Gindi
Harry Gindi
15:46
@TomerSchlank I could swear I saw this in Riehl-Verity
but I don't remember where
Rune Haugseng
Rune Haugseng
16:04
@TomerSchlank To identify with unstraightening, can't you just say that this pullback is the right fibration for the composite C -> PSh(C) -> S, where the second functor corresponds to the fibration PSh(C)/F -> PSh(C) and so is just Map(-, F); Yoneda then identifies the composite with F. But maybe that assumes more than you wanted to?
Harry Gindi
Harry Gindi
@RuneHaugseng that was the proof i had in mind from Cisinski's book, but yeah I wasn't sure if this is what he wants
 
5 hours later…
Praphulla Koushik
Praphulla Koushik
21:16
Suppose we have following diargam
A_1 --> C_1 <-- B_1
| | |
| | |
v v v
A_2 --> C_2 <-- B_2
I dont know how to write diargam clearly in chat... Horizantal arrows are correct.. vertical arrows are from A_1 to A_2, C_1 to C_2 and B_1 to B_2...
supose vertical arows are epimorphjisms... does that confirm that the induced map on pul backs A_1 \times_{C_1} B_1 ---> A_2 \times_{C_2} B_2 is an epimorphism??
I have a proof that assumes A_1 to A_2 and B_1 to B_2 are epimorphisms and C_1 to C_2 is monomorphism.. can some one tell me if this is true even if C_1 to C_2 is just an epimorphism
thanks
 
2 hours later…
William Balderrama
William Balderrama
23:07
@PraphullaKoushik if I understand your question correctly, the diagram of sets where everything but C1 is a singleton, and C1 is the coproduct of A1 and B1, gives a counterexample.

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