ScalingStacks

Conjecture 3 [03UM]

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Conjecture 3

The map πm​e​r\pi_{mer} is well-defined and extends by continuity to the map π:Xa​n→B\pi:{X}^{an}\to B. The set Bs​mB^{sm} (defined as the maximal open subset of BB on which the limiting metric is smooth) coincides with the set of π\pi-smooth points. Two 𝐙{\bf Z}-affine structures on Bs​mB^{sm}, one coming from the collapse picture, another coming from non-archimedean picture, coinside with each other.

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