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?

@TomerSchlank I could swear I saw this in Riehl-Verity

but I don't remember where

@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?

@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

Suppose we have following diargam

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

@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.