9:48 AM
Hey, has anyone ever inspected SAG Theorem 1.4.8.1?
It seems kinda fishy to me.
There's a missing reference to the key step as well. Is this filled in elsewhere (like one of the DAG papers)?
The reason it seems fishy to me is that, at least if you're doing something really stupid and obvious, it's not true that the affine schemes étale over the spdm stack X are 0-truncated objects.
So what this seems to be saying is that if you have a spdm stack (X,O_X), and you take the spdm stack (X,π_0(O_X)), which is some kind of ordinary higher Deligne-Mumford stack, there always exists a 'coarse moduli DM-1-stack' for the discrete (but still higher-dimensional) Deligne-Mumford stack (X,π_0(O_X)).