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Apr 28, 2019 at 17:16 vote accept CommunityBot
Apr 1, 2019 at 11:26 comment added Jason Starr @AknazarKazhymurat. Certainly the construction above does not give that. The problem here, and with the previous MathOverflow question, is that the stack in groupoids of proper, smooth schemes is not an algebraic stack (I explain why in my article on "Artin's axioms, composition and moduli spaces"). Thus, each of these constructions of "countable families" that represent each geometric point are ad hoc. There is no reason for these ad hoc constructions to have any good properties.
Mar 30, 2019 at 10:43 comment added user74900 can we also require that for each $i$ there exists a $\mathbb{C}$-immersion $X_i\rightarrow X_{i+1}$ inducing an isomorphism on $\mathbb{Z}$-singular cohomology of the associated complex analytic spaces (in cohomological degrees$\leq 2i$)?
S Mar 30, 2019 at 9:42 history answered Jason Starr CC BY-SA 4.0
S Mar 30, 2019 at 9:42 history made wiki Post Made Community Wiki by Jason Starr